We studied the structural, spin-polarized electronic band structures, density of states, and magnetic properties of the diluted magnetic semiconductors (DMSs) Cd1-xMnxS and Cd1-xMnxS in zinc blende phase (B3) with 25% Mn by using the ab initio method. The calculations were performed by using the full potential linearized augmented plane wave plus local orbitals (FP-L/APW+lo) method within the spin-polarized density functional theory and the local spin density approximation (LSDA). Calculated electronic band structures and the density of states of these DMSs are discussed in terms of the contribution of Mn 3d(5)4s(2), Cd 4d(10)5s(2), S 3s(2)3p(4), and Se 4s(2)4p(4) partial density of states and we also compute the local magnetic moments. We estimated the spin-exchange splitting energies, Delta(x)(d) and Delta(x)(p-d), produced by the Mn 3d states, and we found that the effective potential for the minority spin is more attractive than that for the majority spin. We determine the s-d exchange constant N-0 alpha and p-d exchange constant N-0 beta, which resembles a typical magneto-optical experiment. The calculated total magnetic moment is found to be 5.0020 and 5.00013 mu(B) for Cd1-xMnxS and Cd1-xMnxSe, respectively. These values indicate that every Mn impurity adds no hole carriers to the perfect CdS and CdSe crystals. Moreover, we found that p-d hybridization reduces the local magnetic moment of Mn from its free space charge value of 5.0 mu(B) and produces small local magnetic moments on the nonmagnetic Cd and S sites.