In　this　paper,　we　investigate　the　leader-following　rendezvous　with　connective　preservation　problem　for　a　class　of　single-integrator　multi-agent　systems　subject　to　a　nonlinear　leader　system.　A　class　of　distributed　nonlinear　internal　model　is　established　and　the　equivalent　cooperative　stabilization　problem　is　solved　by　a　potential　function　based　nonlinear　distributed　controller.　It　is　interesting　that　this　nonlinear　stabilizer　has　the　ability　of　maintaining　the　network　connectivity.　The　theoretical　result　is　also　illustrated　by　a　simulation　example.　©　2017　IEEE.