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For a general link linear model (GLLM), we show that the OLS estimate of the slope vector is strongly consistent up to a multiplicative scale, even though the model might actually be nonlinear. Furthermore, the estimated slope vector is strongly consistent for the average slope vector, the average of the pointwise slope vectors on the response surface. For a GLLM with a completely specified link function, we can solve for the multiplicative scalar and estimate the intercept and Cox and Snell's generalized residuals. We then estimate the response surface and the pointwise slopes using a generalization of the smearing estimate in Duan (1983). The results can be applied to a number of important subclasses of GLLM, including general transformation models, general scaled transformation models, dichotomous regression, and Tobit regression.