The crystal-field splittings of the monopnictides and monochalcogenides of cerium (CeX and CeY) and their alloys (CeX_1-xY_x) are calculated by means of an ab initio many-body combined technique. The hybridization functions of the 4f states of cerium with the conduction band for each material are obtained from first principles within the local-density approximation and are used as input for the Anderson impurity model, which is solved within a multiorbital noncrossing approximation. This realistic theoretical approach is able to reproduce the experimental results for the crystal-field splittings of the CeX and CeY series in agreement with previous theoretical calculations. It is also able to describe the nonlinear evolution of the splittings in the CeX_1-xY_x alloys as a function of x. An analysis of the values of the crystal-field splittings in all the compounds can be done in depth in this contribution due to a detailed knowledge of the band structure and crystal environment in combination with many-body physics.