Wide bandgap III-V nitrides, such as GaN and AlN, have become topical in the near-term technology of blue lasers. We report detailed electronic band-structure calculations for (AlN)
 zinc-blende superlattices (SL), with m + n ≤ 12, using the all-electron full-potential linear-muffin-tin-orbital method. For n ≥ 3, the SL are found to have a direct band gap. For n ≤ 2 and m ≥ 3, all the band gaps are indirect. In ultrathin SL, m ≤ 3 and n ≤ 2, only (m, n)= (3,1) is found to have an indirect gap. The band offsets are estimated by calculating the core-level shifts of nitrogen atoms in the central planes of the GaN and A1N layers. The calculated densities of states, electron- and hole- effective masses (m), etc., as a function of m and n, are reported; a remarkable dependence of m on the number of layers is revealed.