A mechanism of the condensation of e-h pairs in bulk GaAs at room temperature, which has been observed earlier, is proposed.The point is that the photon assisted pairing happens in a system of electrons and holes that occupy energy levels at the very bottoms of the bands. Due to a very high e-h density, the destruction of the pairs and loss of coherency does not occur because almost all energy levels inside a 30-60 meV band from the bottom of the conduction band prove to be occupied. As a result, a coherent ensemble of composite bosons (paired electrons and holes) with the minimum possible energy appears. The lifetime of this strongly non-equilibrium coherent e-h BCS-like state is as short as a few hundred of femtoseconds. In the high-density limit, collectively paired electrons and holes behave like Cooper pairs in a superconductor, and the BCS-like energy gap at the Fermi level is the order parameter of the macroscopic quantum state [1,6]. As noted before [7], the order parameter of the excitonic condensate is identical to its optical polarization and can be directly accessed by relatively simple optical measurements. Moreover, it has been theoretically predicted that the dephasing and relaxation kinetics of excitonic condensate depends on its density in some cases [7]. In particular, the polarization dephasing rate slows down with increasing density of the condensate. This implies that the destruction of coherency due to collisions does not happen despite of an enhanced collision rate with increasing density.In our recent experiments [8][9][10][11], we have studied the regime of the cooperative recombination in a highly non-equilibrium large density (> 3 . 10 18 cm -3 ) system of electrons and holes in bulk GaAs at room temperature.The main information about the properties of the electron-