1 Introduction Consider i.i.d. observations ( x$_{i}$ , y$_{i}$ ) , i = 1 , ..., n, given by the nonlinear model with random predictors: where x$_{i}$ ∈ R q and e$_{i}$ are independent, and the unknown parameter vector θ$_{0}$ ranges in a set Θ ⊂ R $^{p}$. An important case, usually called separable , are models where p = p$_{1}$ + p$_{2}$ and θ$_{0}$ = ( α$_{0}$, β$_{0}$ ) with α$_{0}$ ∈ A ⊂ R p 1 and β$_{0}$ ∈ B ⊂ R p 2 , and g of the form where h$_{j}$ ( j = 1 , ..., p$_{2}$ ) are functions of X × R p 2 → R. Usually B is the whole of R p 2 or an unbounded subset of it. Examples are the Michaelis-Menten model, with the logistic growth model, with the exponential decay model, with and the exponential growth model, like (5) but with α$_{j}$ > 0 . The classical least squares estimate (LSE) is given by 2 ̂ θ = arg min θ ∈ Θ n ∑ i =1 ( y$_{i}$ − g ( x$_{i}$ , θ )) 2 . q = 1 , p$_{2}$ = p$_{1}$ + 1 , x ≥ 0 , α$_{j}$ < 0 , β$_{j}$ ≥ 0 , g ( x , α, β ) = β$_{0}$ + p 1 ∑ j =1 β$_{j}$e α$_{j}$$^{x}$, (5) q = 1 , p 2 = 1 , p$_{2}$ = 1 , x ≥ 0 , α$_{j}$ > 0 , β > 0 , h ( x , α ) = e α 2 x 1 + α$_{1}$ ( e α 2 x − 1) , (4) p$_{1}$ = p$_{2}$ = q = 1 , x ≥ 0 , α, β > 0 , h ( x, α ) = x x + α , (3) g ( x , θ ) = g ( x , α, β ) = p 2 ∑ j =1 β$_{j}$h$_{j}$ ( x , α ) , (2) y$_{i}$ = g ( x$_{i}$ , θ$_{0}$ ) + e$_{i}$, (1)