Translational diffusion of fluorescent molecules on curved surfaces (micelles, vesicles, and proteins) depolarizes the fluorescence. A Monte Carlo simulation method was developed to obtain the fluorescence anisotropy decays for the general case of molecular dipoles tilted at an angle alpha to the surface normal. The method is used to obtain fluorescence anisotropy decay due to diffusion of tilted dipoles on a spherical surface, which matched well with the exact solution for the sphere. The anisotropy decay is a single exponential for alpha=0 degrees, a double exponential for alpha=90 degrees, and three exponentials for intermediate angles. The slower decay component(s) for alpha not equal 0 arise due to the geometric phase factor. Although the anisotropy decay equation contains three exponentials, there are only two parameters, namely alpha and the rate constant, D-tr/R-2, where D-tr is the translational diffusion coefficient and R is the radius of the sphere. It is therefore possible to determine the orientation angle and translational diffusion coefficient from the experimental fluorescence anisotropy data. This method was applied in interpreting the fluorescence anisotropy decay of Nile red in SDS micelles. It is necessary, however, to include two other independent mechanisms of fluorescence depolarization for molecules intercalated in micelles. These are the wobbling dynamics of the molecule about the molecular long axis, and the rotation of the spherical micelle as a whole. The fitting of the fluorescence anisotropy decay to the full equation gave the tilt angle of the molecular dipoles to be 1 +/- 2 degrees and the translational diffusion coefficient to be 1.3 +/- 0.1x10(-10) m(2)/s.