  We establish a general criterion which ensures exponential mixing of
parabolic Stochastic Partial Differential Equations (SPDE) driven by a non
additive noise which is white in time and smooth in space. We apply this
criterion on two representative examples: 2D Navier-Stokes (NS) equations and
Complex Ginzburg-Landau (CGL) equation with a locally Lipschitz noise. Due to
the possible degeneracy of the noise, Doob theorem cannot be applied. Hence a
coupling method is used in the spirit of [EMS], [KS3] and [Matt]. Previous
results require assumptions on the covariance of the noise which might seem
restrictive and artificial. For instance, for NS and CGL, the covariance
operator is supposed to be diagonal in the eigenbasis of the Laplacian and not
depending on the high modes of the solutions. The method developped in the
present paper gets rid of such assumptions and only requires that the range of
the covariance operator contains the low modes.
