  The standard Eliashberg - McMillan theory of superconductivity is essentially
based on the adiabatic approximation. Here we present some simple estimates of
electron - phonon interaction within Eliashberg - McMillan approach in non -
adiabatic and even antiadiabatic situation, when characteristic phonon
frequency $\Omega_0$ becomes large enough, i.e. comparable or exceeding the
Fermi energy $E_F$. We discuss the general definition of Eliashberg - McMillan
(pairing) electron - phonon coupling constant $\lambda$, taking into account
the finite value of phonon frequencies. We show that the mass renormalization
of electrons is in general determined by different coupling constant
$\tilde\lambda$, which takes into account the finite width of conduction band,
and describes the smooth transition from the adiabatic regime to the region of
strong nonadiabaticity. In antiadiabatic limit, when $\Omega_0\gg E_F$, the new
small parameter of perturbation theory is
$\lambda\frac{E_F}{\Omega_0}\sim\lambda\frac{D}{\Omega_0}\ll 1$ ($D$ is
conduction band half -- width), and corrections to electronic spectrum (mass
renormalization) become irrelevant. However, the temperature of superconducting
transition $T_c$ in antiadiabatic limit is still determined by Eliashberg -
McMillan coupling constant $\lambda$. We consider in detail the model with
discrete set of (optical) phonon frequencies. A general expression for
superconducting transition temperature $T_c$ is derived, which is valid in
situation, when one (or several) of such phonons becomes antiadiabatic. We also
analyze the contribution of such phonons into the Coulomb pseudopotential
$\mu^{\star}$ and show, that antiadiabatic phonons do not contribute to
Tolmachev's logarithm and its value is determined by partial contributions from
adiabatic phonons only.
