Effects associated with the penetration of an electric field $E$ into a superconductor with deviations from thermodynamic equilibrium are considered. The penetration of a static field $E$ incident to the passage of a current across the boundary between the superconductor and the normal metal ($S$-$N$ boundary) is analyzed. At temperatures close to the critical temperature the penetration depth $I_\mathrm{E}$ of a field $E$ into the $S$ region may be much greater than the correlation length or the London depth and may reach macroscopic dimensions in sufficiently pure specimens. In isotropic superconductors the magnitude of $I_\mathrm{E}$ is determined by the branch imbalance relaxation processes. The change in the gap width at the $S$-$N$ boundary leads to an additional branch imbalance relaxation mechanism which, in pure specimens, is due to Andreev reflection of quasiparticles. The resistance of a superconductor in the intermediate state is calculated. Weakly damped collective oscillations with an acoustic spectrum, which exist in superconductors near the critical temperature, are considered. This collective mode is characterized by oscillations of both the field $E$ and the branch imbalance. The propagation velocity of the oscillations is somewhat lower than the Fermi velocity. Effects associated with the penetration of the field $E$ to great depths in Josephson bridges are analyzed. The theory of the phenomena considered is presented, using the kinetic equation and the equations for the Green's functions. Experiments are described for measuring effects associated with the penetration of a static field $E$ into a superconductor and for detecting the collective oscillations.