A. V. Gaponov-Grekhov was engaged in solving this problem for 6 years and in 1955 defended his PhD thesis on "Electromechanical systems with sliding contacts and dynamic theory of electrical machines" at the Leningrad Polytechnic Institute.

For these thesis A. V. Gaponov-Grekhov was immediately awarded the degree of a Doctor of Sciences in Physics and Mathematics due to the significance of his work.

A. V. Gaponov-Grekhov's younger brother was Sergey V. Gaponov (1937-2024), also a physicist, a Full Member of the Russian Academy of Sciences.

Since the late 1950s, A. V. Gaponov-Grekhov has been engaged in intense research in the field of nonlinear wave processes, as well as in solving the problem of generating and amplifying high-power high-frequency electromagnetic oscillations in the millimeter and submillimeter wavelength ranges.

Gyrotrons, the devices developed on these principles, have found application in thermonuclear reactors and tracking of space objects.

On the basis of these works, together with his co-workers, he created cyclotron resonance masers, which are high-power generators of the millimeter and submillimeter electromagnetic waves.