Local minima on the singlet, triplet, and quintet potential energy surfaces (PES) of cobalt and copper mononitrosyls are studied by DFT with the B3LYP functional. While quintet states are separated from the triplet and singlet states by a high energy gap, the linear singlet local minimum and the triplet transition state of CoNO lie close together. The ordering of local minima by relative stability of low-lying excited states with respect to the ground state was assessed by B3LYP, the coupled-cluster method CCSD(T), and complete active space calculations (CAS MP2). The ground state of CoNO is (3)A'; two local minima were found in singlet states: linear, and side-on configuration, (1)A(1). The occurrence of bound states on the triplet and singlet PES of CoNO and CuNO was examined by CASSCF. The crossing of the singlet and triplet PES of CoNO is a conical intersection; the geometry of the bound state is linear, with elongated N-O bond. The activation energy for the spin-forbidden transition (3)A' -> (1)Sigma(+) is estimated to be 154.7 kJ mol(-1). For CuNO, the triplet and singlet PES do not cross but are separated by a small energy gap. Copper nitrosyl is of lower thermodynamic stability than cobalt nitrosyl. A triplet ground state (3)A '' with bent configuration is predicted by B3LYP, confirmed by CAS MP2, and a very close-lying singlet state (1)A' is found with nearly identical geometry. Unlike CoNO, the linear triplet CuNO in (3)Sigma(-) state is not a transition state, but a local minimum, lying close to the dissociation limit Cu + NO. Vibrational frequencies are calculated for the gas-phase molecules and for the metal nitrosyl entrapped in solid Ar matrix. Under the influence of the noble gas matrix, the energy gap between the singlet and the triplet CuNO is reduced, and the singlet and triplet states of bent CuNO become nearly isoenergetic in agreement with experimental data. The linear CoNO in (1)Sigma(+) state is the most stable configuration in the Ar matrix, with one Ar atom coordinated to the metal center.