The Bose–Einstein condensation of excitons in two-dimensional (2D) systems has been studied theoretically, taking into account both the random potential associated with imperfections of the structure and the finite exciton lifetime. It is shown that the disorder existing in the system makes condensation possible. The finite exciton lifetime limits the thermalization of excitons in the disordered system and sets an additional limit on the critical temperature of the transition. The effects of interparticle interaction and pump fluctuations have been analyzed. The phase correlator has been calculated and the failure of the condensate due to the effects of interaction and fluctuations has been analyzed. The propagation of perturbations in the condensate has been investigated.