  We show results on propagation of anisotropic Gabor wave front sets for
solutions to a class of evolution equations of Schr\"odinger type. The
Hamiltonian is assumed to have a real-valued principal symbol with the
anisotropic homogeneity $a(\lambda x, \lambda^\sigma \xi) = \lambda^{1+\sigma}
a(x,\xi)$ for $\lambda > 0$ where $\sigma > 0$ is a rational anisotropy
parameter. We prove that the propagator is continuous on anisotropic
Shubin--Sobolev spaces. The main result says that the propagation of the
anisotropic Gabor wave front set follows the Hamilton flow of the principal
symbol.
