  We study the localization of classical waves in weakly scattering 2D systems
with anisotropic disorder. The analysis is based on a perturbative
path-integral technique combined with a spectral filtering that accounts for
the first-order Bragg scattering only. It is shown that in the long-wavelength
limit the radiation is always localized, and the localization length is
independent of the direction of propagation, the latter in contrast to the
predictions based on an anisotropic tight-binding model. For shorter
wavelengths that are comparable to the correlation scales of the disorder, the
transport properties of disordered media are essentially different in the
directions along and across the correlation ellipse. There exists a
frequency-dependent critical value of the anisotropy parameter, below which
waves are localized at all angles of propagation. Above this critical value,
the radiation is localized only within some angular sectors centered at the
short axis of the correlation ellipse and is extended in other directions.
