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It is shown that the famous Allen -- Dynes asymtotic limit forsuperconducting transition temperature in very strong coupling region$T_{c}>\frac{1}{2\pi}\sqrt{\lambda}\Omega_0$ (where $\lambda\gg 1$ - isEliashberg - McMillan electron - phonon coupling constant and $\Omega_0$ - thecharacteristic frequency of phonons) in antiadiabatic limit of Eliashbergequations $\Omega_0/D\gg 1$ ($D\sim E_F$ is conduction band half-width and$E_F$ is Fermi energy) is replaced by $T_c>(2\pi^4)^{-1/3}(\lambdaD\Omega_0^2)^{1/3}$, with the upper limit for $T_c$ given by$T_c<\frac{2}{\pi^2}\lambda D$.

Temperature of superconducting transition for very strong coupling in antiadiabatic limit of Eliashberg equations