  A random flight on a plane with non-isotropic displacements at the moments of
direction changes is considered. In the case of exponentially distributed
flight lengths a Gaussian limit theorem is proved for the position of a
particle in the scheme of series when jump lengths and non-isotropic
displacements tend to zero. If the flight lengths have a folded Cauchy
distribution the limiting distribution of the particle position is a
convolution of the circular bivariate Cauchy distribution with a Gaussian law.
