We prove that the inequality partial derivative P/partial derivative v
< 0 is the stability criterion for dark solitons of the one-dimension
al nonlinear Schrodinger equation with general nonlinearity. Here v is
the soliton's velocity, and P renormalized momentum: P = (i/2) integr
al(psi(x)psi - psi(x) psi*)(1 - (rho 0)/\psi\(2))dx.