First-principle FLAPW-GGA band structure calculations are employed to obtain the structural, electronic properties and chemical bonding picture for two related layered phases, namely, quaternary oxyarsenides LaZnAsO and YZnAsO. These compounds are found to be direct-transition type semiconductors with the GGA gaps of about 0.65-1.30 eV. The peculiarities of chemical bonding in these phases are investigated and discussed in comparison with quaternary oxyarsenide LaFeAsO - a basic phase for the newly discovered 26-52K superconductors.