A theoretical study of the first-row transition metal dicarbide cations MC2+ (M = Sc-Zn) has been carried out. Predictions for different molecular properties that could help in their eventual experimental detection have been made. Most MC2+ compounds prefer a C-2v symmetric arrangement over the linear geometry. In particular, the C-2v isomer is specially favored for early transition metals. Only for CuC2+ is the linear isomer predicted to be the global minimum, although by only 1 kcal/mol. In all cases the isomerization barrier between cyclic and linear species seems to be very small (below 2 kcal/mol). The topological analysis of the electronic density shows that most C-2v isomers are T-shaped structures. In general, MC2+ compounds for early transition metals have larger dissociation energies than those formed by late transition metals. In most cases the dissociation energies for MC2+ compounds are much smaller than those obtained for their neutral analogues. An analysis of the bonding in MC2+ compounds in terms of the interactions between the valence orbitals of the fragments helps to interpret their main features.