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This paper studies the theory and design of a class of perfect reconstruction (PR) causal-stable nonuniform recombination cosine modulated filter banks (RN CMFB) with IIR filters. It is based on the RN CMFB previously proposed by one of the authors. A PR FIR RN CMFB of similar specification is first designed. The prototype filters of the CMFB are then model reduced to obtain a nearly PR (NPR) IIR RN CMFB by modifying a model reduction technique proposed by Brandenstein and Unbehauen (1998). With these NPR IIR RN CMFB as initial guess, PR IIR RN CMFB with very good frequency characteristics can be obtained readily by solving a constrained nonlinear optimisation problem using for example the function fmincom from MATLAB. Design results show that the proposed method is very effective in designing PR RN IIR CMFB with good frequency characteristics and different system delays.