This paper considers the estimation of the parameters of a non-linear regression equation. Instead of the usual assumptions about the first and second moments of the error distribution, the assumption is made that the p.d.f. of the convolution of this distribution and the normal distribution has a unique global maximum. Conditions are given so that the estimator obtained is strongly consistent and asymptotically normally distributed and attention is paid to its asymptotic efficiency. Moreover, the method is extended to the multivariate case.