25 ILCS 10/2

The Speaker of the House and the President of the Senate, and the Chairman and members of the Senate Committee on Committees shall be considered as holding continuing offices until their respective successors are elected and qualified.

In the event of death or resignation of the Speaker of the House or of the President of the Senate after the sine die adjournment of the session of the General Assembly at which he was elected, the powers held by him shall pass respectively to the Majority Leader of the House of Representatives or to the Majority Leader of the Senate who, for the purposes of such powers shall be considered as holding continuing offices until his respective successors are elected and qualified.