We present first-principals all-electrons total-energy calculations concerning structural and electronic properties for the group III-V zinc-blend-like compounds AlN, GaN and InN using the full-potential linearized augmented plane wave (FP-LAPW) approach within the density functional theory (D.F.T) in the local density approximation (L.D.A) and the generalized gradient approximation (G.G.A) for the exchange correlations functional. Moreover, we have calculated bulk properties, including ground-state energies, lattice parameters, bulk modulus, its derivatives, cohesive energy and band structures. We find that the GGA yields improved physical properties for bulk AlN compared to the LDA. For GaN and InN, essentially no improvement is found: the LDA exhibits over binding, whereas the GGA shows a tendency for under binding. The degree of under binding and the overestimation of lattice parameters as obtained within the GGA increase on going from InN to GaN. Band structures are found to be very similar within the LDA and the GGA, for AlN, GaN and InN, therefore, the GGA does not offer any significant advantages.