Elezi was apprehended at the Bulgarian-Macedonian border in July 2005. He was extradited to the United States by a Bulgarian court.
Elezi was accused of being the leader of an international network to smuggle hundreds of immigrants from countries in Eastern Europe, such as Albania and Macedonia, via Bulgaria and then Mexico to the United States.
The indictments say the aliens paid as much as $16,000 to get to the United States.
Elezi faces a maximum of 80 years in prison, if convicted on all charges.