A new investigation of the dependence of the period-luminosity (PL) and period-luminosity-color (PLC) relations on the helium and metal abundances in classical Cepheids is presented. Composition dependences are assigned to all quantitites under study, so that the results represent a true theoretical prediction. It is found that the PLC relation in B,V magnitudes is at least five times more sensitive to chemical composition than is the PL relation. If the PL relation is adopted and the helium abundance is held fixed, a Cepheid with Z = 0.005 should be fainter than one with Z = 0.02 by about 0.04 mag. Since the slope of the predicted PL relation is independent of chemical composition, the PL relation can be considered to be effectively universal. Additional supporting observational evidence is described, and theoretical results are also presented for the bolometric PL relation, whose slope and dependence on metal abundance should be roughly applicable to infrared observations of Cepheids.