  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
($\sim 100$ 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 $\aplt 60$ 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 $\sim
30$ 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.
