Dynamical scaling in phase-ordering kinetics is well-accepted. We consider the possibility of a larger dynamical symmetry (called local scale-invariance) for this non-equilibrium relaxation phenomenon. Indeed, in many systems with and without detailed balance the Langevin equation can be decomposed into a `deterministic' and a `stochastic' part in such a way that if the `deterministic' part is Galilei-invariant, then the calculation of the full noisy response and correlation functions reduces exactly to the calculation of certain n-point functions calculable within the `deterministic' part of the theory. Galilei- and Schroedinger-invariant equations will be constructed. This leads to explicit predictions for the two-time response and correlation functions, in good agreement with simulational results and with the results of several exactly solvable models.