Abstract : The authors employ a quadratic expansion to investigate the behavior of the ordinary residuals in nonlinear regression. In particular, they derive quadratic approximations for the mean and variance of the ordinary residuals, and the covariances between the ordinary residuals and the fitted values. This investigation leads to the conclusion that the ordinary residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression. Consequently, a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals is suggested. (Author)