The interactions of neutral and ionic copper atoms with molecular oxygen and nitric oxide have been examined by using relativistic effective core potentials (ECP) and different ab initio MO methods up to the coupled cluster CCSD(T) approach. For neutral CuO2 the ECP calculations reproduce the results of all-electron calculations which prefer the "side-on" structure by 0.9 kcal/ mol versus an "end-on" coordination. The binding energy for the "side-on" complex ((2)A(2)) has been calculated to be 9.7 kcal/mol. For the cationic end-on CuO2+ ((3) Sigma(+)) an identical binding energy (9.7 kcal/mol) results from CCSD(T) calculations; the side-on complex (B-3(1)) is 4 kcal/mol less stable. The singlet state ((1)A’) of the cation is 27 kcal/mol higher in energy and bound with 13.6 kcal/mol with respect to singlet oxygen (((1) Delta(g)(+)) and Cu+ (S-1), while the side-on ((1)A(1)) state is 3.8 kcal/mol less stable than the (1)A’ state. For the interaction of neutral Cu with NO the end-on CuNO coordination ((1)A’) with a bonding energy of 10.4 kcal/mol is preferred while the related triplet ((3)A") is 5.5 kcal/mol less stable. In the cationic system [Cu,N,O](+), both isomers, i.e., CuNO+ and CuON+ represent stable species, with CuNO+ ((2)A’) being the more stable one. The bond dissociation energies of these two isomers are calculated to 19.3 and 11.4 kcal/mol, respectively.