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Brayan, 16, at the Central American Refugee Center in Hempstead, N.Y., in June. Brayan crossed into the United States last year.Credit Andrew Renneisen for The New York Times

Wearing Vans shoes and rubber band bracelets, hair gel and shy smiles, the brothers Brayan and José looked like typical teenagers.

But the story they told of their turbulent past year revealed just how far from typical they have traveled.

In separate trips, the boys explained, they left El Salvador to avoid being recruited by violent gangs and trekked across two countries. They were caught by United States Border Patrol agents in Texas in 2014 and sent to different detention centers for several weeks before being reunited in Elmont, N.Y., with their father, Arturo. They had not seen him in 10 years.

“That’s why I brought them one at a time,” Arturo said in Spanish at the Long Island offices of the boys’ immigration lawyer, “because if something happened to one, at least I would have the other.” The family requested that their last name not be used because of their legal status.

Like thousands of other children who fled the violence gripping several Central American countries, Brayan, now 16, and José, 15, arrived safely in the United States only to spend the next 13 months navigating the justice system to prove they have a right to stay.

They have missed many days of school to appear in federal immigration court and state family court, helped their father complete a pile of paperwork taller than them and have contended with bureaucratic requirements that seemed endless.

Last summer, President Obama declared a crisis along the border with Mexico in response to the tens of thousands of unaccompanied children coming into the country. Detention centers in Texas overflowed, prompting the federal Department of Homeland Security to open emergency shelters. Political tempers boiled over — Rick Perry, who was the governor of Texas, ordered 1,000 National Guard troops to defend the border. The Obama administration created a priority juvenile docket in immigration courts to speed up deportation proceedings.

One year later, the number of children arriving at the border has slowed dramatically, in part because Mexico has been returning children to their home countries before they can reach the United States.

But the crisis has not ended. It has simply shifted. It is playing out in courtrooms crowded with young defendants but lacking lawyers and judges to handle the sheer volume of cases. Thousands of children without lawyers have been issued deportation orders, some because they never showed up in court.

“The situation last summer was characterized as part of the overall immigration system being broken and it’s taken us down the wrong policy path,” said Wendy Young, the president of Kids In Need of Defense, a national legal advocacy group. “This is not an immigration crisis, it’s a refugee crisis.”

About 84,000 children were apprehended at the Southwest border during the 2014 fiscal year and the first six months of the 2015 fiscal year, according to the Border Patrol. Of the 79,088 removal cases initiated by the government, 15,207 children had been ordered deported as of June, according to the Migration Policy Institute, a nonpartisan research group in Washington.

While a small percentage of children have been granted asylum, most are seeking relief from deportation by applying for special immigrant juvenile status, federal officials said. And yet, rather than their claims being expedited, the majority of the children in the priority docket — 69 percent — still have cases pending, statistics show.

The burden is far more difficult for children if they do not have a lawyer — a right not granted to defendants in immigration courts — especially because of the accelerated time frame the government established for their cases. After being released to a sponsor, usually a relative, they are on the clock: They are required to make their first court appearance within 21 days of the court receiving their case to contest their deportation.

Legal Advantages in New York City

By all accounts, the legal advantages for child immigrants in New York City are more favorable than in other parts of the country where they settled in large numbers, including Los Angeles, South Florida and the Houston area. Last summer, nonprofit agencies and pro bono lawyers formed a coalition at the federal court in Lower Manhattan, backed by $1.9 million in financing from the City Council and private philanthropy, to help those without lawyers.

Although the Council said the coalition took on 648 cases of the 1,600 children screened at 26 Federal Plaza, not all were from the five boroughs and only those children in New York City were eligible for free assistance. Even then, only those who were most likely to win relief could be helped.

“We may have it a little under control in New York City,” said Jojo Annobil, director of immigration for Legal Aid, “but it’s not under control in Long Island,” where, along with Westchester County and the Lower Hudson Valley, large numbers of the children have also settled.

It is a disparity that underscores the contentious divide over what to do about the country’s 11 million undocumented immigrants.

Federal officials defended their approach. Gillian Christensen, a spokeswoman for United States Immigration and Customs Enforcement, said the agency’s lawyers work “with advocates for the children, to ensure that these cases are processed in as expeditious and fair a manner as possible.’’

But Mark Krikorian, the executive director of the Center for Immigration Studies, a Washington research institute that supports tighter controls on immigration, said the process for asylum or special immigration status served as a “rationale for family reunification” and is inherently flawed.

“It’s not that it should be more convoluted, it’s that the standards should be higher,” Mr. Krikorian said. “You’ve got family court judges deciding U.S. immigration policy.”

A Winding Path Through Courts

On a recent day on the 14th ^{floor of 26 Federal Plaza, lawyers bustled around with files, holding hushed and rushed conversations in Spanish with their clients. Inside the courtrooms, the judges presided like school principals; they praised some children for their good grades and implored those without lawyers to seek help on the 12th floor.}

More than a dozen of the teenagers who came to New York City and Long Island recounted their hardships — adjusting to living with estranged parents, having to learn English, taking tests. They asked not to have their full names published because of their undocumented status.

Of the two main paths to winning relief from deportation, asylum is the most straightforward, but also the most difficult to obtain. Children must persuade a federal asylum officer that they face life-threatening persecution based on race, religion, nationality or membership to a political or social group.

Because those cases are difficult to prove, many children, instead, seek relief under special immigrant juvenile status, provided they can show they were abused, neglected or abandoned by one or both parents.

The process requires going through three different entities for approval: federal immigration court, state family court and the federal citizenship agency.

“It means that no one entity in the process can crack the whip or control the flow,” said Lenni Benson, a professor and director of the Safe Passage Project at New York Law School, which mentors volunteer lawyers working on youth immigration cases.

Brayan’s and José’s case shows just how complex the journey can be.

They must prove to the family court they cannot return to El Salvador because one parent abandoned them there. The court must also approve of their guardian — even if, as in the case of Brayan and José, the guardian is their father.

Their father, Arturo, must try to get consent to be the guardian from the boys’ mothers — two different women who he said each abandoned her son in El Salvador.

Different lawyers are handling different parts of the case. David Williams, 31, an immigration lawyer from the Central American Refugee Center, a nonprofit legal provider in Hempstead, N.Y., is preparing their case for federal court. He acted as a liaison for Janet Millman, who represented the brothers in family court in Nassau County and was appointed by the state’s Attorneys for Children panel, which provides legal services for children in family courts.

Mr. Williams and Ms. Millman tried to notify both mothers of their son’s hearings. Neither woman responded from her last known address.

The judge then requested that they put advertisements in newspapers in the United States and in El Salvador, and provide copies of the papers. Still, there was no word from either mother.

Arturo, 44, also had to list every address he has had for the last 28 years so New York State, according to immigration lawyers, can investigate whether he has ever lived with a sex offender.

Although Arturo is an undocumented immigrant, the family court required that he be fingerprinted, along with other members of the household. And when one member moved, the entire household was required to be fingerprinted again.

“It’s confusing and there are times that I’ve had to redo paperwork,” Arturo said.

Finally, when the lawyers had submitted all of the documentation to the court and the family appeared in early July, the judge postponed her decision because she had an unusually full caseload.

Too Many Cases, Too Few Lawyers

Arturo, a car washer, was lucky to get a lawyer at the Central American Refugee Center. Had he arrived weeks later, the organization would have turned the family away because all four of the group’s immigration lawyers had hit their maximum number of 40 cases.

“I don’t want to sound coldhearted,” Patrick Young, the program director of the organization, said, “but we can’t handle it.”

Atlas: DIY, a community-based group serving immigrant children in Brooklyn, stopped taking clients three months ago. To make the most of her resources, the one lawyer on staff, Rebecca McBride, 30, must turn away children whose cases she deems too hard to win because they do not qualify for relief.

She took the case of Elicia, a 17-year-old from Honduras, soon after she was ordered deported in absentia last October.

“For me, it was all over,” Elicia said in Spanish. “I didn’t know if they were going to get me at home or at school.”

When she arrived in July 2014, Elicia did not go to her immigration hearings because friends warned her she could be deported just by showing up in court. But Ms. McBride reopened the case and argued for Elicia to get special juvenile status because her father had neglected and abandoned her. With three days to spare, the judge terminated Elicia’s deportation order.

For more than a year, Brayan and José lived in a similar limbo. It was still better than living in El Salvador.

“These two kids couldn’t go to school, they didn’t know whether they were going to be dead the next day, their life was worth not a whole lot,” Ms. Millman said. “They came because they want to live.”

Last week, a family court judge in Nassau County granted both boys special immigrant juvenile status.

But they are not in the clear. They still must submit applications for green cards to the United States Citizenship and Immigration Services. On Sept. 9, an immigration court judge in Manhattan will rule on whether to cancel their deportation orders.

“It is still a case that is not 100 percent won,” Arturo said. “We still have to give it a little more effort.”