The geometries and thermochemistry of Re2(NO)4(CO) n (n = 4, 3, 2, 1, 0) structures isovalent with the binuclear cobalt carbonyls Co2(CO) n+4 have been examined using density functional theory. Eight low-energy Re2(NO)4(CO)4 structures, all with formal Re-Re single bonds, lie within 6kcalmol(-1) of the global minimum. These eight structures include unbridged structures as well as structures with two bridging NO groups but no structures with bridging CO groups. Similarly, five low-energy Re2(NO)4(CO)3 structures, all with formal Re=Re double bonds, lie within 6kcalmol(-1) of the global minimum. Again these five structures include unbridged structures as well as structures with one or two bridging NO groups but no structures with bridging CO groups. The Re2(NO)4(CO) n (n = 4, 3) appear to be fluxional systems similar to the well-known Co2(CO)8 for which doubly bridged and unbridged structures have approximately the same energies. The lowest energy Re2(NO)4(CO)2 structures have formal Re=Re double bonds including a structure with a five-electron donor bridging η(2)-μ-NO group. Isomeric Re2(NO)4(CO)2 structures with formal Re≡Re triple bonds lie approximately ∼10kcalmol(-1) above the global minimum. For the more highly unsaturated Re2(NO)4(CO) and Re2(NO)4 systems, the lowest energy structures have formal Re≡Re triple bonds of length ∼2.6Å. Higher energy Re2(NO)4(CO) structures have shorter Re-Re distances of length ∼2.5Å suggesting formal quadruple bonds. Graphical Abstract The geometries and thermochemistry of Re2(NO)4(CO) n (n = 4, 3, 2, 1, 0) structures isovalent with the binuclear cobalt carbonyls Co2(CO) n+4 have been examined using density functional theory. A number of energetically closely spaced Re2(NO)4(CO)4 and Re2(NO)4(CO)3 structures are found, including unbridged and NO-bridged structures but no CO-bridged structures. The Re2(NO)4(CO) n (n = 2, 1, 0) systems provide examples of Re-Re multiple bonds of orders ranging from 2 to 4.