The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, (omega) , is in resonance between two subbands in the conduction band. The probe light of the frequency (Omega) falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband (Omega) -light absorption spectra are related to the critical points of the bands, rearranged by the (omega) - light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond (Omega) -light pulses following each other with the delay time, (tau) d. The dependence of energy, absorbed from the second pulse, on the (tau) d value is calculated. Under the (omega) -pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/(omega) R or oscillations with the frequency approximately (omega) R, where (omega) R is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the (Omega) -light pulse.