Search for new half-metallic ferromagnetic binary compounds composed of alkaline earth and III (boron) or IV (carbon) elements is reported. Ab initio all-electron density functional theory calculations in the generalised gradient approximation indicate possibility of half-metallic ferromagnetism. This is a new class of theoretically predicted hypothetical materials, without transition metal elements, not as yet discovered experimentally. Ferromagnetism is expected to be induced by suitable crystalline structure with lattice constant above some critical value. The predominant p electrons mechanism seems to be responsible for the formation and interactions of localised magnetic moments on boron or carbon atoms.