I discuss the interplay between non-Fermi liquid behaviour and superconductivity near a quantum-critical point (QCP) in a metal. It is widely thought that the tendency towards superconductivity and towards non-Fermi liquid behaviour compete with each other, and if the pairing interaction is reduced below a certain threshold, the system displays a naked non-Fermi liquid QC behaviour.  I show that the situation is more complex as there are multiple solutions for Tc at a QCP.  For all solutions, except one, Tc vanishes when the pairing interaction drops below the threshold.   However, there exists one solution, for which Tc  remains finite even when the pairing interaction is arbitrary small, as in BCS theory,  despite that there is no Cooper logarithm. I argue that superconductivity below this finite Tc is induced by fermions with the first Matsubara frequency.  I present explicit results for Tc for the set of models with frequency-dependent effective interaction and discuss the behaviour below Tc, particularly of the density of states and the spectral function.   I argue that there are two qualitatively different regimes of “gap closing” and “gap filling” and relate the second regime to the pairing induced by fermions with the first Matsubara frequency.