  We consider the Markov process defined by some pseudo-differential operator
of the order $1<\alpha<2$ as the process generator. Using a pseudo-gradient
operator, that is, the operator defined by the symbol
$i\lambda|\lambda|^{\beta-1}$ with some $0<\beta<\alpha$, the perturbation of
the Markov process by the pseudo-gradient with a multiplier integrable at some
great enough power is constructed. Such perturbation defines a family of
evolution operators, the properties of which are investigated.
