In Illinois, any species listed federally (even due to only their "similarity of appearance"-- S/A) requires an IDNR endangered/threatened species permit to legally possess them in Illinois. It is my understanding that IDNR is no longer issuing permits for those federally listed crocodilian species to individuals anymore for pets. The number of either escapes or intentional releases by irresponsible keepers because they cannot maintain these animals when they become too large to handle, has risen over the past couple years.
The federal exhibitor's license does not apply to reptiles because USDA has stated that reptiles (and other cold-blooded animals) are not regulated under the Animal Welfare Act. Therefore having a federal exhibitor's license does not "allow" you to have a crocodilian species regulated by IDNR permit. USDA does not even issue those licenses in regards to reptiles. Here is a link to that:
http://www.aphis.usda.gov/publications/animal_welfare/content/printable_version/fs_awexhibitr.pdf
Therefore if it is your wish to legally keep a crocodilian as a pet in Illinois, I would recommend looking into keeping something that does not appear on the federal list, such as maybe a dwarf caiman.
However, also understand that while this outlines state law, any smaller local unit of government (such as a county or municipality) CAN be more restrictive than the state. So you may also want to check into any local county or city/village laws where you live to see if they have any regulations regarding the keep of crocodilians as pets. Your local and county animal control officer could answer that question for you.
Scott