  The possibility is indicated of applying the theory of superconductors with
overlapping energy bands to describe the thermodynamic and electromagnetic
properties of the high-temperature compounds $La_{2-x}(Ba,Sr)_xCuO_4$ and
$YBa_2Ci_3O_{7-\delta}$. The two-band model was used to obtain high values of
$T_c$, two energy gaps $2\Delta_1/T_c > 3.5$ and $2\Delta_2/T_c < 3.5$, large
negative values of $d\ln T_c/d\ln V$ ($V$ is the volume) in lanthanum ceramics,
small values of the jump in the electron heat capacity at $T=T_c$, negative
curvature of the upper critical magnetic field $H_{c2}$ near the transition
temperature, etc. Such behavior of the above quantities is observed
experimentally. A description is also obtained of the decrease in $T_c$ as the
disordering of oxygen increases, and also as copper atoms are replaced by a
nonmagnetic impurity (Al, Zn, etc.). The main mechanism responsible for this
decrease is the interband scattering of electrons by impurities and by randomly
distributed oxygen vacancies. A theory has been developed of multiband
superconductors which takes into account the points of high symmetry in
momentum space. On the basis of this theory one can explain the existence of a
plateau in the dependence of $T_c$ on $\delta$ for $YBa_2Cu_3O_{7-\delta}$, and
also in the dependence of $T_c$ on $x$ for $La_{2-x}(Ba,Sr)_xCuO_4$, that has
been observed in a number of experiments. Moreover, this theory also explains
the presence of two maxima in the dependence of $T_c$ on pressure for
$Bi_2Sr_2CaCu_2O_8$.
