In regression models, the underlying theory frequently leads to specification of more than one functional form for the conditional mean of the response. The main problem in such cases is whether the differences between the models are sufficiently large relative to the variance of the disturbance term to warrant efforts to discriminate between the models or collect new data in order to discriminate. This paper, after refining the notion of differences between models, suggests several alternative statistics which might be useful in this problem and derives their asymptotic distributions.