  Building on an analogy with conformal invariance, local scale transformations
consistent with dynamical scaling are constructed. Two types of local scale
invariance are found which act as dynamical space-time symmetries of certain
non-local free field theories. The scaling form of two-point functions is
completely fixed by the requirement of local scale invariance. These
predictions are confirmed through tests in the 3D ANNNI model at its Lifshitz
point and in ageing phenomena of simple ferromagnets, here studied through the
kinetic Ising model with Glauber dynamics.
