Excitations of Cooper pairs into non-condensed bound pairs are similar to excitations of true bosons out of the Bose-Einstein condensate. Using the Landau criterion of superfluidity we evaluate the critical current above which these pair-excitations would lead to a finite resistivity. The predicted value strongly depends on the chosen approximation. The Thouless approach based on the Galitskii T-matrix and the Kadanoff-Martin theory which is in many aspects equivalent to the BCS theory, both lead to zero critical velocity, what is in conflict with the mere existence of supercurrents. In contrast, the T-matrix with multiple scattering corrections provides the critical velocity of pair excitation which is √3-times larger than the critical velocity of pair breaking. This agrees with the experimentally well established fact that supercurrents in type I superconductors are limited by pair breaking, not by pair excitation.