We present a pseudopotential study within the local-density formalism of the structural and electronic properties of zinc-blende BN and BP. The ground-state properties of these systems such as bulk moduli, lattice constants, cohesive energies, and frequencies of the TO phonon mode are in good agreement with experimental results. The valence charge density of BP shows two local maxima along the bond, which is similar to the case of diamond. In contrast, the charge density of BN is similar to that of a typical III-V compound semiconductor. The resulting band structures have some important features which are in disagreement with previously published work. Like most III-V compound semiconductors, the fundamental gap in BP decreases with decreasing volume. The corresponding gap in BN, however, increases with decreasing volume as was also found in diamond.