Statistics of estimates of bicoherence and biphase were obtained from numerical simulations of nonlinear random (harmonic) processes with known true bicoherence and biphase. Expressions for the bias, variance, and probability distributions of estimates of bicoherence and biphase as functions of the true bicoherence and number of degrees of freedom (dof) used in the estimates are presented. The probability distributions are consistent with theoretical distributions derived for the limit of infinite dof and are used to construct confidence limits on estimates of bicoherence and biphase. Maximum likelihood estimates of true values of bicoherence and biphase given observed values are also presented. ¿ American Geophysical Union 1989