In this paper, we present an internal model approach for the leader-following rendezvous and connectivity preservation problem for a class of multi-agent systems, where both the follower and leader systems can be assumed to contain the strong nonlinearity, as well as the external disturbances and the parametric uncertainties. With the suitable choice of the potential function, two types of internal model based distributed controllers are developed for handling both cases of the certain and uncertain leaders, respectively. By innovatively constructing the intrinsical nonlinear relationship between the rendezvous error and the virtual rendezvous error, we can obtain the corresponding gain functions in both controllers that are able to conquer not only the strong nonlinearity of control plant but also the nonlinearity caused by the potential function. Finally, the validity of our design is illustrated by an example. (C) 2017 Elsevier Ltd. All rights reserved.