  The phase diagram of two-dimensional systems with continuous symmetry of the
vector order parameter containing defects of the "random local anisotropy" type
is investigated. In the case of a weakly anisotropic distribution of the easy
anisotropy axes in the space of the order parameter, with decreasing
temperature, a smooth transition takes place from the paramagnetic phase with
dynamic fluctuations of the order parameter to the Imri-Ma phase with its
static fluctuations. In the case when the anisotropic distribution of the easy
axes induces a global anisotropy of the "easy axis" type that exceeds a
critical value, the system goes into the Ising class of universality, and a
phase transition to the ordered state occurs in it at a finite temperature.
