In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei,1in under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.