The potential curves and spectroscopic constants of the excited states of alkali-argon diatomics MRg (M=Li, Na and K, Rg=Ar) are calculated using usual semilocal single valence electron pseudopotentials on alkali atoms [M+]-core pseudopotentials), semilocal pseudopotentials replac(ing all the electrons of argon ([Ar]-core pseudopotentials), and core polarization pseudopotentials on both centers. All states dissociating into Li(2s, 2p, 3s, 3p, 3d, 4s, and 4p), Na(3s, 3p, 3d, 4s, 4p, 4d, 5p) and K(4s, 4p, 5s, 3d, 5p, 4d, 6s, 4f, 6p, 5d, 7s, 5f) are considered. The core-core interactions for Li+Ar and Na+Ar are included using the accurate ab initio potentials of Ahmadi [G. R. Ahmadi, J. Almlof, and I. Roeggen, Chem. Phys. 199, 33 (1995); G. R. Ahmadi and I. Roeggen, J. Phys. B 27, 5603 (1994)] while the K+Ar ion data are determined by MP2 all-electron calculations.