The potential energy curves of the X, A, and B states of alkali-rare gas diatomic molecules, MKr and MXe, are investigated for M = Li, Na, K. The molecular spin-orbit coefficients a(R)=〈(2)Π(12)|Ĥ(SO)|(2)Π(12)〉 and b(R)=〈(2)Π(-12)|Ĥ(SO)|(2)Σ(12)〉 are calculated as a function the interatomic distance R. We show that a(R) increases and b(R) decreases as R decreases. This effect becomes less and less important as the mass of the alkali increases. A comparison of the rovibrational properties deduced from our calculations with experimental measurements recorded for NaKr and NaXe shows the quality of the calculations.