  A self-consistent, adiabatic model for the {\it long-time} behaviour of tidal
capture binaries is presented. It is shown that most capture orbits behave
chaotically, with the eccentricity following a quasi-random walk between the
values of $\appless 1$ and some lower limit associated with the periastron
separation at capture.
  If dissipation is taken into account, the binary goes through a short and
violent chaotic phase, followed by a long quiescent phase in which it slowly
circularizes from a high eccentricity on a much longer timescale than
previously thought. A consequence is that merger is less likely than previously
thought, and hence such binaries will be available as a heat source to the
cores of globular clusters, particularly while they are in the less tightly
bound, highly eccentric phase.
  If the model is correct, any highly eccentric binaries observed in globular
clusters which contain a main-sequence star will most likely be found to have a
period derivative much smaller than that predicted by the standard model.
  We also predict that the companion of PSR B1718-19 in NGC 6342 which is a
globular cluster binary likely to have been formed by tidal capture (Wijers \&
Paczy\'{n}ski 1993) will be found to have a mass of around $0.2M_\odot$.
  The model may be used to describe the evolution of low-mass X-ray binaries,
pulsar binaries, and cataclysmic binaries which abound in globular clusters.
