The singlet and triplet states of AlCu and AlAg below about 32 000 cm(-1) are studied using the internally contracted multireference configuration-interaction method. A more elaborate study of the X (1) Sigma(+) ground state of AlCu is undertaken using extended Gaussian basis sets, including the effect of inner-shell correlation and including a perturbational estimate of relativistic effects. Our best estimate of the spectroscopic constants (r(0), Delta G(1/2), and D-0) for the X (1) Sigma(+) state with the experimental values in parentheses are : 4.416(4.420) a0, 295(294) cm(-1), and 2.318(2.315) eV. The calculations definitively assign the upper state in the observed transition at 14 892 cm(-1) to the lowest (1) Pi. state. The calculated spectroscopic constants and radiative lifetime for the (1) Pi state are in good agreement with experiment. The calculations support the tentative assignments of Behm et al. for three band systems observed in the visible region between 25 000 and 28 000 cm(-1). However, the computed spectroscopic constants are in very poor agreement with those deduced from an analysis of the spectra. Analogous theoretical results for AlAg suggest that the (2)(3) Pi, (3)(3) Pi, and (3)(1) Sigma(+) states account for the bands observed, but not assigned, by Duncan and co-workers.