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)$_x$CuO$_4$ and YВа$_2$Сi$_3$О$_{7-\delta}$. 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