By means of adiabatically eliminationg the upper level or levels of a A-configuration atom coupling to a two-mode quantized field, we have studied the influencesofac Stark shifts on the atomic coherent population trapping in two important atom-field coupling systems via nondegenerated Raman two-photon processes.The states of the field that trap the atom in its two nondegenerate lower levels are obtained, and the important roles of ac Stark shifts and properties of the atomic upper level or levels in the states of the trapping field in two Raman-coupling systems are also analyzed.