We study the evolution of bound pairs of star clusters by means of direct N-body simulations. Our simulations include mass loss by stellar evolution. The initial conditions are selected to mimic the observed binary star cluster NGC 2136 and NGC 2137 in the Large Magellanic Cloud. Based on the rather old ages (∼100 Myr), masses, sizes of the two clusters and their projected separation, we conclude that the cluster pair must have been born with an initial separation of 15-20 pc. Clusters with a smaller initial separation tend to merge in ∼< 60 Myr due to loss of angular momentum from escaping stars. Clusters with a larger initial separation tend to become even more widely separated due to mass loss from the evolving stellar populations. The early orbital evolution of a binary cluster is governed by mass loss from the evolving stellar population and by loss of angular momentum from escaping stars. Mass loss by stellar winds and supernovae explosions in the first ∼30 Myr causes the binary to expand and the orbit to become eccentric. The initially less massive cluster expands more quickly than the binary separation increases, and is therefore bound to initiate mass transfer to the more massive cluster. This process is quite contrary to stellar binaries in which the more massive star tends to initiate mass transfer. Since mass transfer proceeds on a thermal timescale from the less massive to the more massive cluster, this semi-detached phase is quite stable, even in an eccentric orbit until the orbital separation reaches the gyration radius of the two clusters, at which point both clusters merge to one.