Abstract: For a regression model for two-stage sampling, the covariance matrix of error vector contains an intracluster correlation ρ. The purpose of this paper is to study the robustness of the least squares estimate （LSE） and that of the likelihood ratio test stutisties （LRTS） with respect to ρ. A set of necessary and sufficient conditions for the robustness of the LSE and a necessary condition and a sufficient condition for that of the LRTS are given respectively.