One measure would ban the sale of semiautomatic handguns and rifles. People who currently own such weapons could keep them, but would have to register them. The second proposal would limit ammunition magazines to 10 or fewer rounds.
Democrats are pushing the gun restrictions in the wake of the school massacre in Connecticut last month.
The bills now go to the full Senate. Governor Pat Quinn has said there is no place in the state for weapons designed to rapidly fire at human targets at close range.