<p>This paper is concerned with a class of uncertain multiobjective semi-infinite programming problems with equilibrium constraints (abbreviated as UMSIPECs). We formulate the robust counterpart of UMSIPEC, that is, the robust multiobjective semi-infinite programming problems with equilibrium constraints (abbreviated as RMSIPEC). To establish the necessary criteria of local robust weak Pareto efficiency for RMSIPEC, we introduce the generalized standard Abadie constraint qualification (abbreviated as GS-ACQ) for RMSIPEC. Moreover, by employing the convexity assumptions, we deduce the sufficient criteria for robust weak Pareto efficiency for RMSIPEC. Furthermore, we formulate the Mond-Weir and Wolfe-type dual problems related to the problem RMSIPEC and derive weak as well as strong duality results that relate the primal problem RMSIPEC and the corresponding dual problems. Suitable examples are provided to illustrate the significance of the results established in this paper. To the best of our knowledge, this is the first time that the optimality conditions and duality results for RMSIPEC have been studied.</p>