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.