We calculate the damping of quadrupole f- and low-order g-modes (primary modes) by nonlinear coupling to other modes of the star. Primary modes destabilize high-degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. For Sun-like stars, the growth time =eta(-1) approximate to 4F(0,42)(1/2) days, where E(0,42) is the initial energy of the primary mode in units of 10(42) ergs, and the number of daughter modes N similar to 10(10)E(0,42)(5/4). The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, delta R/R* approximate to 0.002E(0.42)(1/2). Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time similar to 10 eta(-1) provided E(0) > 10(40) ergs. This is orders of magnitude smaller than usual radiative damping time. In fact, nonlinear mode interaction may be the dominant damping process if E(0) greater than or similar to 10(37) ergs. These results have obvious application to tidally captured main-sequence globular cluster stars of mass greater than or equal to 0.5 Mo.; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the initial orbital period. Nonlinear mode coupling is a less efficient damping process for fully convective stars, which lack g-modes. In convective stars, most of the tidal energy is in the quadrupole f-modes, which nonresonantly excite high-order p-modes of degree 0, 2, and 4. The resultant short-wavelength waves are more efficiently dissipated. The nonlinear damping time for f-modes is shown to be proportional to 1/E(0); this damping time is about 30 days for E(0) approximate to 10(45) ergs expected in tidal captures. However, at such a large energy the system is very nonlinear: 4-mode and higher order couplings are as important as 3-mode couplings.
