Abstract. In this paper we present a robust duality theory for gener-alized convex programming problems under data uncertainty. Recently,Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362–1373]established a robust duality theory for generalized convex programmingproblems in the face of data uncertainty. Furthermore, we extend re-sults of Jeyakumar, Li and Lee for an uncertain multiobjective robustoptimization problem. 1. IntroductionConsider the standard nonlinear programming problem with inequality con-straints(P) inf x∈R n {f(x) : g i (x) <= 0, i = 1,...,m},where f : R n → Rand g i : R n → Rare continuously differentiable functions.The problem in the face of data uncertainty in the constraints can be capturedby the following nonlinear programming problem:(UP) inf x∈R n {f(x) : g i (x,v i ) <= 0, i = 1,...,m},where v i is an uncertain parameter and v i ∈ V i for some convex compact setV i in R q and g i : R n ×R q → Ris continuously differentiable. Robust optimiza-tion, which has emerged as a powerful deterministic approach for studyingmathematical programming under uncertainty ([4]-[5], [6]), associates with theuncertain program (UP) its robust counterpart [1],(RP) inf