Welcome to Autodesk Forums!

Hi,

Curved objects in most cases come as splines when imported from AI. If they are closed, than in theory you should be able to extrude it. So at first verify that they are closed and doesn't self-intersect.
You can also try to convert splines from AI to Polylines with PEDIT command before extruding them.
Can you attach sample AI file you have troubles with?

Maxim