  We theoretically study the upper critical magnetic fields at zero temperature
in a quasi-two-dimensional (Q2D) superconductor in the parallel and
perpendicular fields, $H_{c2}^{\parallel}(0)$ and $H_{c2}^{\perp}$(0),
respectively. We find that $H_{c2}^{\parallel}(0) \approx 0.75 \ | d
H_{c2}^{\parallel}/ dT|_{T_c} T_c $ and that $H_{c2}^{\perp}(0) \approx 0.59 \
| dH_{c2}^{\perp}/ d T|_{T_c} T_c$, where $| d H_{c2}^{\parallel}/ dT|_{T_c}$
and $| d H_{c2}^{\perp}/ d T|_{T_c}$ are the corresponding Ginzburg-Landau
slopes of the upper critical magnetic fields. Our results demonstrate the
breakdown of the so-called effective mass model in Q2D case and may be
partially responsible for the experimentally observed deviations from the
effective mass model in a number of layered superconductors, including $MgB_2$.
