We have performed ab initio self-consistent calculations of the standard cohesive properties (equilibrium lattice parameters, binding energies and bulk moduli) of the four alkali-earth oxides (MgO, CaO, SrO and BaO) having the B1 (NaCl-like) phase under normal temperature and pressure conditions. We have also studied the relative stability of the B1 and B2 (CsCl-like) phases, and the behaviour, under pressure of these crystals (equations of state, transition pressures and changes of volume for the structural phase transition ). All the calculations were performed in the framework of the density-functional theory by a method which allows the direct calculation of the ground-state electron density of a system without the preliminary determination of its wavefunctions and energy eigenvalues.