Speaker separation is a special case of speech separation, in which the mixture signal comprises two or more speakers. Many talker-independent speaker separation methods have been introduced in recent years to address this problem in anechoic conditions. To consider more realistic environments, this paper investigates talker-independent speaker separation in reverberant conditions. To effectively deal with speaker separation and speech dereverberation, extending the deep computational auditory scene analysis (CASA) approach to a two-stage system is proposed. In this method, reverberant utterances are first separated and separated utterances are then dereverberated. The proposed two-stage deep CASA system significantly outperforms a baseline one-stage deep CASA method in real reverberant conditions. The proposed system has superior separation performance at the frame level and higher accuracy in assigning separated frames to individual speakers. The proposed system successfully generalizes to an unseen speech corpus and exhibits similar performance to a talker-dependent system.