Abstract.A theory of quasi-stationary spectrum of electrons interacting with electromagnetic field of arbitrary intensity in an open two-barrier resonance tunnel structure is developed using exact solution of the complete Schrödinger equation. It is shown that, besides the quasi-stationary electronic states having usual resonance energies and widths, additional satellite quasi-stationary states appear in the spectrum, with their resonance energies located near the resonance energies of every of the quasi-stationary states at the distances being multiples of an energy fixed by the electromagnetic field frequency.