  We study the purely relaxational critical dynamics with non-conserved order
parameter (model A critical dynamics) for three-dimensional magnets with
disorder in a form of the random anisotropy axis. For the random axis
anisotropic distribution, the static asymptotic critical behaviour coincides
with that of random site Ising systems. Therefore the asymptotic critical
dynamics is governed by the dynamical exponent of the random Ising model.
However, the disorder influences considerably the dynamical behaviour in the
non-asymptotic regime. We perform a field-theoretical renormalization group
analysis within the minimal subtraction scheme in two-loop approximation to
investigate asymptotic and effective critical dynamics of random anisotropy
systems. The results demonstrate the non-monotonic behaviour of the dynamical
effective critical exponent $z_{\rm eff}$.
