We propose a memory form of exchange-correlation potential vXC(r, t) for time-dependent interacting many-particle systems. Unlike previous memory-XC potentials, our vXC is not limited to the linear response regime. The proposed form of vXC is a generalized local-density approximation chosen so as to satisfy the nonlinear harmonic potential theorem and Newton’ s third law. For the case of the inhomogeneous electron gas, we give an explicit prescription for vXC based solely on an existing parametrization of the linear XC response kernel fhomXC(n, ω) of the uniform gas. Application to quantum wells seems promising.