The generation of terahertz radiation in the dimensional-confined structures has attracted a great deal of attention recently. The importance of the exciton states in the process of terahertz radiation generation, especially when the pump acts in the exciton range of spectrum was denoted. This is important also because the time dephasing of the excitons is much greater than the time dephasing of noncorrelated electrons and holes. We propose a new mechanism of terahertz radiation generation (amplification) in bulk or dimensional-confined semiconductor structures which is based on the use of quantum transitions between exciton and biexciton states. These states can play an important role in the process of terahertz radiation generation. Let the incident pulse of resonant laser radiation on the semiconductor with the frequency ω1 equal to the frequency of exciton transition, excites the excitons from the ground state of the crystal. We consider the excitonic state to be macroscopically occupied. The two-exciton state is also macroscopically occupied. Therefore the inversion of population appears between two-exciton and biexciton states. And if we inject a weak pulse of terahertz radiation of frequency ω2, equal to frequency of quantum transitions between two-exciton and biexciton states, then such a radiation will be amplified because of the induced downthrow of the inversion. From the interaction Hamiltonian of both the waves with excitons and biexcitons we obtain the Heisenberg equation of motion for the amplitudes of the exciton and biexciton waves. Using the steady-state regime we determine the susceptibilities of the medium for the range of frequencies of exciton state and two-exciton–biexciton conversion. Both susceptibilities contains the dispersive (real) and absorptive (imaginary) components. For every resonance detuning we have negative absorptive component for frequency of quantum transitions between two-exciton and biexciton states and positive for frequency of exciton level. Consequently, the propagating radiation with the frequency ω2 in the medium will be amplified and the one with the frequency ω1 will become weak. In the slowly varying envelope approximation we obtain the set of nonlinear equations for determining of the spatial distribution of the field amplitudes along the direction of propagation which shows that the nonlinear coefficient of light absorption at the frequency ω1 and the enhancement coefficient at the frequency ω2 strongly depend on the intensity of both waves. We did not obtain the exact analytical solutions of this set of equations. But in case of the exact resonance, in the linear approximation on the intensity of first wave and then integrating the set wave equations, we obtain the integral of motion which gives the connection between the intensities of both waves in every point of crystal. This integral shows that the intensity of low-frequency wave depends exponentially upon the intensity of high-frequency wave. The enhancement coefficient of low-frequency wave has the maximal value at the front bound of crystal and it is proportional to the square of initial intensity of wave on the frequency ω1. It decreases monotonously with the increasing of intensity of terahertz radiation. So is showed that the population inversion between two-exciton and biexciton states appears at the pumping of the exciton state, on the transition between which the generation of terahertz radiation is possible. The intensity of the terahertz radiation increases with the increase of the pump intensity.