We review and elaborate on the issue of the dilaton transformation under the usual r --> alpha'/r target space duality and its "non-static" generalization (or sigma-model duality). It is found that the transformation law r --> alpha'/r, phi --> phi-In(r/square-root-alpha') which guarantees duality at the one-loop sigma-model level should be modified at two (and higher) loop order. The "non-static" duality is illustrated on the example of "cosmological" solutions in D greater-than-or-equal-to 2 with time-dependent radii of space torus.