The hyperfine coupling constants (hfcc) and electron-spin g-factors (magnetic moments) calculated for B-2(+), Al-2(+), Ga-2(+), BAl+, BGa+, and AlGa+ are reported. The hfcc's are obtained with single-reference configuration interaction, second-order Moller-Plesset, density functional (B3LYP, PW91PW91) methods, and 6-311+G(2df ) basis sets. The 2sigma(g)/3sigma SOMOs of X (2)Sigma(g)(+)(1sigma(g)(2)1sigma(u)(2)2sigma(g))/X (2)Sigma(+)(1sigma(2)2sigma(2)3sigma) mainly have a p(sigma)-p(sigma) composition, leading in most cases to similar values of A(dip) and A(iso). As a result, \A(parallel to)\ is up two orders of magnitude larger than \A(perpendicular to)\. The A(perpendicular to)'s are slightly negative (ca. -10 MHz) for Al-2(+), Ga-2(+), and AlGa+. The g-shifts (Deltag=g-g(e)) are evaluated with multireference CI wave functions, perturbation expansions up to second-order, and 6-311+G(2d) basis sets. Both Deltag(parallel to) and Deltag(perpendicular to) are negative, but Deltag(parallel to) lies close to zero. The Deltag(perpendicular to)'s of B-2(+), Al-2(+), Ga-2(+) are about -1 300, -12 800, -97 300 ppm, respectively, while for BGa+, BAl+, AlGa+, they are much smaller (-800, -2 800, -47 400 ppm). The reduced Deltag(perpendicular to)'s for XY+ result from the mutual cancellation between a positive contribution from the 1 (2)Pi(3sigma-->1pi) state but a negative one from 2 (2)Pi(3sigma-->2pi). The positive contribution is at variance with the rule-of-thumb stating that SOMO-->virtual MO excitations should contribute negatively. The variation of the hfcc's with bond distance is analyzed for all systems, and that of the Deltag(perpendicular to) component for B-2(+) and BAl+. Experimental or previous theoretical electron-spin resonance data are not available for comparison.