We study nucleation of kink-antikink pairs under weak nonequilibrium conditions and in the strong friction limit. We introduce an effective critical nucleus of size s0, which is small compared to the inverse kink density but large compared to a kink size. We evaluate independently the nucleation rate and the kink lifetime from a multidimensional Kramers theory and by studying kink-antikink annihilation processes. We find a kink density which is independent of s0 and of the driving force in this regime. The result is in accordance with the equilibrium kink density obtained from statistical mechanics.