( CNN ) -- The Libyan government argued Tuesday that it should not have to hand over Saif al-Islam Gadhafi to the International Criminal Court because the court in the Hague , Netherlands , does not have jurisdiction in the case . Gadhafi , son of deposed strongman Moammar Gadhafi , was facing an arrest warrant from the ICC for alleged crimes against humanity at the time of his capture in November 2011 . The court is still seeking to prosecute him and wants him handed over . Gadhafi has been held in the Libyan city of Zintan since his capture . The two-day hearing is being held in the Hague . Read more : Libya granted more time on Gadhafi question . The ICC has demanded that Libya hand Gadhafi over to face accusations of crimes against humanity . Libya appealed the decision , saying that he should be tried at home . Court-appointed attorneys Melinda Taylor and Xavier-Jean Keita said in April that Gadhafi has been mistreated and `` physically attacked '' since his capture . Live blog : Gadhafi releases taped message . In a strongly worded statement , the lawyers described Gadhafi as being in a legal black hole , held in total isolation except for visits from officials . He also suffers dental pain because he has n't had treatment , and Libyan authorities have given him nothing to remedy the pain , the lawyers said . The Libyan government wants to prosecute Gadhafi itself , as it `` regards the trial of Saif al-Islam and Abdullah al-Senussi as a matter of the highest national importance , not only in bringing justice for the Libyan people but also in demonstrating that the new Libyan justice system is capable of conducting fair trials ( that meet all applicable international standards ) in complex cases . '' Al-Senussi , who was Libya 's chief of intelligence under Moammar Gadhafi 's , is wanted by both the ICC and the Libyan government . He was arrested in Mauritania in March . Read more : Libyans celebrate capture of Gadhafi 's son Saif al-Islam . The appeal document also seeks to answer ICC concerns about Saif al-Islam Gadhafi 's well-being , saying the government `` has expended considerable resources in order to ensure the safe and secure temporary custody '' of Gadhafi in Zintan and is negotiating to bring him to the capital , where facilities would be better . Amnesty International has previously called on Libya to hand over Gadhafi . `` An unfair trial before a Libyan court where the accused could face the death penalty is no way to guarantee justice and accountability , '' the rights group said . Amnesty has said that Libya does not have a functioning court system and the country was `` unable to conduct effective investigations , '' so `` the ICC will be crucial in delivering accountability in Libya . '' Libya and the ICC have been going back and forth since his capture about where Saif al-Islam Gadhafi , once his father 's heir apparent , will be tried . Moammar Gadhafi died after his capture by opposition forces a year ago .
The two-day hearing is scheduled to run through Wednesday . Libyan authorities want to try the son of late strongman Moammar Gadhafi in Libya . TL;DR NEW: