We report the results of density functional theory calculations on chromium oxide clusters responding to the formula CrmOn (m = 1-2, n = 1-3). Double numeric basis sets supplemented by polarization functions have been used in both local and nonlocal spin density approximations. Geometry optimizations of different spin states have been performed at the unrestricted spin level for the selected initial configurations. We have found that the covalent polarized Cr-O bonds dominate the chemical description of the CrOn series, while for the Cr2On series the presence of the Cr-Cr bond reduces the metal to oxygen charge transfer, yielding much softer clusters, as reflected by the smaller HOMO-LUMO gaps. The stability of all the isomers has been checked by computing their harmonic vibrational frequencies and the energetics of different fragmentation paths. The calculations reveal that the linear isomers are not true minima and that the oxygen-rich clusters are preferred over the metal-rich clusters. Overall, our results show good agreement with the available experimental data in terms of geometrical parameters, vibrational frequencies, atomization energies, and fragmentations for the CrOn clusters. For the Cr2O series, our computed values are discussed in connection with recent infrared spectroscopy measurements and with available data in analogous metal oxide clusters.