We present an algorithm for rapid evolution of binary stars. This incorporates single star evolution based on simple fitting formulae that cover a wide range in mass and metallicity. Mass loss, Roche mass transfer and common-envelope evolution are followed with the changes applied to both the primary and secondary where applicable. Due to the large radii of giants the binary evolution is most interesting when AGB stars are involved. We describe the properties of the remnants of binary interaction during the AGB phase and discuss the consequences for a population of AGB stars. We have implemented the algorithm into an N-body code where we also include collisions between stars, either single or binary. We discuss the implications for both dynamical evolution of star clusters and conversely for the evolution of the binaries themselves.