The diagnostic properties of residuals based on generalized rank-based (GR) estimates are investigated. These are bounded-influence estimates which are resistant to the effects of outliers in either the y- or x-space. Using first order approximations based on asymptotic linearity results, the interpretation of residuals based on GR-fits is discussed for true and misspecified models. A measure of departure from othogonality of both R- and GR-residuals and their corresponding fitted values is also proposed. This measure and the interpretation of GR-residuals prove insightful in an understanding of GR-residual plots. Proper standardization of GR-residuals is also discussed. This is effective in declaration of potential outliers. A small Monte Carlo study along with examples verify the asymptotic theory .