  We study asymptotic behavior of one-step weighted $M$-estimators based on
samples from arrays of not necessarily identically distributed random variables
and representing explicit approximations to the corresponding consistent
weighted $M$-estimators. Sufficient conditions are presented for asymptotic
normality of the one-step weighted $M$-estimators under consideration. As a
consequence, we consider some well-known nonlinear regression models where the
procedure mentioned allow us to construct explicit asymptotically optimal
estimators.
