The Texas teenager derided for a claim of "affluenza" as a defence for a deadly drunken-driving crash, won a delay of weeks for a return to Texas from Mexico, while his mother was in a Los Angeles jail on Thursday after being deported.

A Mexican court has granted fugitive Ethan Couch, 18, an injunction against his deportation, delaying his return by weeks or months, a Mexican migration official said on Thursday.

Couch and his mother, Tonya Couch, 48, were captured in the Mexican Pacific Coast resort city of Puerto Vallarta on Monday. They fled there after officials in Tarrant County, Texas, began an investigation into whether Ethan violated the probation deal that kept him out of prison after he killed four people with his pickup truck in 2013.

Ethan Couch's case would now be subject to immigration proceedings because he entered the country illegally, but he would ultimately not be able to stay in the country, said the Mexican official, who spoke on condition of anonymity.

Tonya Couch, who was wanted on a charge of hindering apprehension, was flown out of Mexico and landed in Los Angeles early Thursday. She could be seen in video coverage being led through the airport in handcuffs.

Tonya Couch is taken by authorities to a waiting car after arriving at Los Angeles International Airport on Thursday following her deportation from Mexico. (Mark J. Terrill/Associated Press)

She is being held without bail in the Metropolitan Detention Center in Los Angeles and would be transferred to Texas, said Los Angeles police spokeswoman Jane Kim. Officials have not announced a date for the move and there is no scheduled court appearance in Los Angeles for the mother, Kim said.

The mother could fight her transfer and may not arrive in Tarrant County until Friday at the earliest, local TV broadcaster WFAA cited county prosecutors as saying. A lawyer for Tonya Couch did not respond to a request to comment.

If convicted of the hindering charge, Tonya Couch could face two to 10 years in prison, Tarrant County Sheriff Dee Anderson said.

"Any roadblock"

Sheriff Anderson said he was not surprised that the pair would seek to drag out their return to Texas.

"They have done everything that they can so far to avoid being accountable, or avoid being brought to justice," he said. "Any roadblock they can put in the way, any hurdle, I fully expect that."

Anderson said when Ethan Couch arrives in the United States, he would appear at a detention hearing in the juvenile system. The judge could keep him in a juvenile detention facility or send him to an adult jail, he said.

During Ethan Couch's trial in juvenile court over the crash in 2013, a psychologist testified on his behalf that he was afflicted with "affluenza," meaning that he was so spoiled by his wealth that he could not tell the difference between right and wrong.

The diagnosis is not recognized by the American Psychiatric Association and was widely ridiculed.

Couch was convicted of four counts of intoxication manslaughter and sentenced to 10 years of drink- and drug-free probation, which critics saw as leniency because of his family's wealth. His flight to Mexico rekindled anger over that sentence.

Couch and his mother fled the United States earlier this month after a video surfaced online apparently showing Ethan Couch at a party where beer was being consumed.

In the car crash, Couch, then 16, was speeding and had a blood-alcohol level nearly three times the legal limit when he lost control of his pickup truck and struck a stranded motorist and three people who had stopped to help.

During their last days in Puerto Vallarta, Couch and his mother lived in a modest apartment, kept a low profile and at least once used a false name as they tried to stay under the radar, local people and neighbours said.