Simple complexes connected through C-H center dot center dot center dot S and C-H center dot center dot center dot N interactions are investigated: CH(4)center dot center dot center dot NH3, C(2)H(4)center dot center dot center dot NH3, C(2)H(2)center dot center dot center dot NH3, CH(4)center dot center dot center dot SH2, C(2)H(4)center dot center dot center dot SH2 and C2H center dot center dot center dot SH2. Ab initio and DFT calculations are performed (SCF, MP2, B3LYP) using different basis sets up to the MP2/aug-cc-pVQZ//MP2/aug-cc-pVDZ level of approximation. The Bader theory is applied since MP2/6-311++G(d,p) wave functions are used to find and to characterize bond critical points in terms of electron densities and their Laplacians. The influence of hybridization on the properties of C-H center dot center dot center dot S and C-H center dot center dot center dot N systems is also studied showing that the strength of such interactions increases in the following order: C(sp(3))-H center dot center dot center dot Y, C(sp(2))-H center dot center dot center dot Y, C(sp)-H center dot center dot center dot Y, where Y = S, N-it is in line with the previous findings on C-H center dot center dot center dot O hydrogen bonds. The results also show that CH(4)center dot center dot center dot SH2 and C(2)H(4)center dot center dot center dot SH2 complexes should be rather classified as van der Waals interactions and not as hydrogen bonds. The frequency associated with the C-H stretch of C(sp(3))-H center dot center dot center dot S is blue-shifted.