  In a second-order r-mode theory, S'a & Tom'e found that the r-mode
oscillation in neutron stars (NSs) could induce stellar differential rotation,
which leads to a saturation state of the oscillation spontaneously. Based on a
consideration of the coupling of the r-modes and the stellar spin and thermal
evolutions, we carefully investigate the influences of the r-mode-induced
differential rotation on the long-term evolutions of isolated NSs and NSs in
low-mass X-ray binaries, where the viscous damping of the r-modes and its
resultant effects are taken into account. The numerical results show that, for
both kinds of NSs, the differential rotation can prolong the duration of the
r-mode saturation state significantly. As a result, the stars can keep nearly
constant temperature and angular velocity over a thousand years. Moreover, due
to the long-term steady rotation of the stars, persistent quasi-monochromatic
gravitational wave radiation could be expected, which increases the
detectibility of gravitational waves from both nascent and accreting old NSs.
