Mexico agreed to transfer El Chapo Guzman in May after the US guaranteed he would not face the death penalty.
However, the ruling means it could be months or even years before the drug lord is sent to the US, where he faces murder and drug smuggling charges.
El Chapo Guzman is being held in a maximum security prison near the US border.
He was arrested in January after six months on the run following his escape through a tunnel in his jail cell. He had already escaped a maximum security facility once before, spending 13 years at large.
One of the appeals argues that the statute of limitations has run out on some crimes El Chapo Guzman is accused of in the US, his lawyer Jose Refugio Rodriguez told Associated Press.
El Chapo Guzman’s defense also argues some of the accusations lack direct evidence.
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