We study Co-x,CryOm+ (x + y = 2, 3 and 1 <= m <= 4) clusters by means of density-functional-theory calculations. It is found that the clusters grow preferentially through maximizing the number of metal-oxygen bonds with a favor on Cr sites. The size- and composition-dependent magnetic behavior is discussed in relation with the local atomic magnetic moments. While doped species show an oscillatory magnetic behavior, the total magnetic moment of pure cobalt and chromium oxide clusters tends to enhance or reduce as increasing the oxygen content, respectively. The dissociation energies for different evaporation channels are also calculated to suggest the stable patterns, as fingerprints for future photofragmentation experiments. (C) 2015 Elsevier B.V. All rights reserved.