  The influence of compressibility on the stability of the scaling regimes of
the passive scalar advected by a Gaussian velocity field with finite
correlation time is investigated by the field theoretic renormalization group
within two-loop approximation. The influence of compressibility on the scaling
regimes is discussed as a function of the exponents $\epsilon$ and $\eta$,
where $\epsilon$ characterizes the energy spectrum of the velocity field in the
inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the
correlation time at the wave number $k$ which is scaled as $k^{-2+\eta}$. The
restrictions given by nonzero compressibility on the regions with stable
infrared fixed points which correspond to the stable infrared scaling regimes
are discussed in detail. A special attention is paid to the case of so-called
frozen velocity field, when the velocity correlator is time independent. In
this case, explicit inequalities which must be fulfilled in the plane
$\epsilon-\eta$ are determined within two-loop approximation. The existence of
a "critical" value $\alpha_c$ of the parameter of compressibility $\alpha$ at
which one of the two-loop conditions is canceled as a result of the competition
between compressible and incompressible terms is discussed. Brief general
analysis of the stability of the scaling regime of the model with finite
correlations in time of the velocity field within two-loop approximation is
also given.
