  The influence of uniaxial small-scale anisotropy on the stability of the
scaling regimes and on the anomalous scaling of the structure functions of a
passive scalar advected by a Gaussian solenoidal velocity field with finite
correlation time is investigated by the field theoretic renormalization group
and operator product expansion within one-loop approximation. Possible scaling
regimes are found and classified in the plane of exponents $\epsilon-\eta$,
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 of the velocity field at the wave number $k$ which is scaled
as $k^{-2+\eta}$. It is shown that the presence of anisotropy does not disturb
the stability of the infrared fixed points of the renormalization group
equations which are directly related to the corresponding scaling regimes. The
influence of anisotropy on the anomalous scaling of the structure functions of
the passive scalar field is studied as a function of the fixed point value of
the parameter $u$ which represents the ratio of turnover time of scalar field
and velocity correlation time. It is shown that the corresponding one-loop
anomalous dimensions, which are the same (universal) for all particular models
with concrete value of $u$ in the isotropic case, are different (nonuniversal)
in the case with the presence of small-scale anisotropy and they are continuous
functions of the anisotropy parameters, as well as the parameter $u$. The
dependence of the anomalous dimensions on the anisotropy parameters of two
special limits of the general model, namely, the rapid-change model and the
frozen velocity field model, are found when $u\to \infty$ and $u\to 0$,
respectively.
