Bilevel optimization problems have received a growing attention in the recent past. In this paper, we suggest methodologies for handling uncertainty in both lower and upper level decision variables that may occur from different practicalities. For the first time, we discuss and demonstrate the effect of uncertainties in each level on the overall definition of a robust bilevel solution and present simulation results on a number of test problems. Finally, the robust solutions of a bilevel circuit design problem are found using a previously suggested fast bilevel evolutionary algorithm (BLEAQ). Definition of robust bilevel solutions, effect of lower and upper level uncertainties in robust bilevel solutions, development of a robust bilevel evolutionary algorithm and simulation results on test and engineering design problems are contributions of this study.