In this paper a robust regulation problem for infinite-dimensional systems with infinite-dimensional exosystems is discussed. The input and output spaces are also allowed to be infinite-dimensional. A new definition of internal model in terms of the controller parameters is given. It is shown that there exists a feedback controller containing an internal model of the exosystem, which robustly regulates the class of signals generated by the exosystem and strongly or weakly stabilizes the closed-loop system. As far as the authors know, the results are new even for finite-dimensional systems with infinite-dimensional exosystems.