The out-of-plane angular dependence of the ferromagnetic resonance linewidth, Delta H, has been measured for thin magnetic films coupled to NiO and for uncoupled control films. In the control films, Delta H is described by nearly angle-independent damping parameters. In the NiO-coupled films, however, the damping was found to depend strongly on magnetization orientation, with linewidth values comparable to the control samples at normal orientation, but several times larger when the magnetization lies in plane. The additional linewidth in the NiO-coupled films follows the angular dependence of the number of nearly degenerate spin wave modes, in agreement with the predictions of a two-magnon scattering model of damping which incorporates a spin wave dispersion relation suitable for ultrathin films. (C) 1998 American Institute of Physics. [S0021-8979(98)37811-1].