  The gravitational-wave and accretion driven evolution of neutron stars in low
mass X-ray binaries and similar systems is analyzed, while the amplitude of the
radiating perturbation (here assumed to be an r-mode) remains small. If most of
the star is superfluid, with (temperature independent) mutual friction
dominating the ordinary (temperature dependent) shear viscosity, the amplitude
of the mode and the angular velocity of the star oscillate about their
equilibrium values with a period of at least a few hundred years. The resulting
oscillation of the neutron star temperature is also computed. For temperature
dependent viscosity, the general conditions for the equilibrium to be stable
are found.
