75 ILCS 5/4-3.1

As the terms of the library trustees elected in any incorporated town or village expire, (except a village under the commission form of government) their successors shall be elected in accordance with the general election law to hold their office for 6 years until their successors are elected and qualified.

Any board may provide by resolution that the term of its trustees shall be 4 years. If the board adopts such a resolution, then if 3 trustees are to be elected at the next election or if 2 trustees are to be elected at each of the next 2 elections, one of the trustees elected at the first election, to be determined by lot at the first meeting after that election, shall serve a 2 year term.