We derive the exact equation of motion for a vortex in two- and three-
dimensional nonrelativistic systems governed by the Ginzburg-Landau eq
uation with complex coefficients. The velocity is given in terms of lo
cal gradients of the magnitude and phase of the complex field and is e
xact also for arbitrarily small intervortex distances. The results for
vortices in a superfluid or a superconductor are recovered.