We propose and theoretically investigate a two-photon four-wave mixing experiment to probe for BoseEinstein condensate of excitons in Cu₂O thin films in which excitons are pumped directly into a state with wave vector k=0 by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the three incident beams, and numerical and approximate analytical solutions are found which describe the time dependence of the exciton and photon densities. When one takes into account the boundary conditions, which result in reflections from the interfaces, the characteristics of the resulting phase-conjugated signal will exhibit Fabry-Perot like oscillations (Fig. 1).Fig. 1. Dependence of of the resulting phase-conjugated signal (arbitrary units) versus time t and film thickness L for the flux density of incident pulses S =1MW / cm² . For film thicknesses equal to a multiple of a half wavelength in the film the resulting signal is enhanced by more than an order of magnitude relative thicknesses that are an odd multiple of a quarter wavelength. In this case the contribution from accompanying excitonic condensates with wave vectors ±2k is minimal. Therefore, the resulting phase-conjugated signal vs. the delay time between the pump and probe pulses yields a direct measure of the time evolution only of the exciton condensate with wave vector k=0. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time td between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time td is the same as the exciton density dependence on the time t. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.