Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + σ(X)ϵ, where m (·) = E(Y||·) belongs to some parametric class {mθ(·):θ∈} of regression functions, σ2(·) = var(Y||·) is unknown, and ϵ is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector θ0 is proposed that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The consistency and asymptotic normality of the proposed estimator are established. The estimator is compared through simulations with an estimator proposed by Stute in 1999, and both methods are also applied to a fatigue life dataset of strain-controlled materials.