  Quasiclassic Uzadel equations for two-band superconductors in the dirty limit
with the account of both intraband and interband scattering by nonmagnetic
impurities are derived for any anisotropic Fermi surface. From these equations
the Ginzburg-Landau equations, and the critical temperature $T_c$ are obtained.
An equation for the upper critical field, which determines both the temperature
dependence of $H_{c2}(T)$ and the orientational dependence of $H_{c2}(\theta)$
as a function of the angle $\theta$ between ${\bf H}$ and the c-axis is
obtained. It is shown that the shape of the $H_{c2}(T)$ curve essentially
depends on the ratio of the intraband electron diffusivities $D_1$ and $D_1$,
and can be very different from the standard one-gap dirty limit theory. In
particular, the value $H_{c2}(0)$ can considerably exceed $0.7T_cdH_{c2}/dT_c$,
which can have important consequences for applications of $MgB_2$. A scaling
relation is proposed which enables one to obtain the angular dependence of
$H_{c2}(\theta)$ from the equation for $H_{c2}$ at ${\bf H}\| c$. It is shown
that, depending on the relation between $D_1$ and $D_2$, the ratio of the upper
critical field $H_{c2}^\|/H_{c2}^\perp$ for ${\bf H}\| ab$ and ${\bf H}\perp
ab$ can both increase and decrease as the temperature decreases. Implications
of the obtained results for $MgB_2$ are discussed.
