This　paper　addresses　the　adaptive　control　of　a　class　of　time-varying　nonlinear　systems.　Under　the　framework　of　Immersion　and　Invariance　(I&I)　adaptive　control,　a　set　of　sufficient　conditions　is　obtained　to　stabilize　the　concerned　time-varying　nonlinear　systems.　It　is　shown　that　the　presented　controller　can　also　be　utilized　to　complete　tracking　control　for　a　class　of　nonholonomic　constraint　systems　if　the　desired　trajectories　satisfy　certain　conditions.　The　effectiveness　of　the　new　adaptive　controller　is　demonstrated　by　some　numerical　simulations　on　a　nonholonomic　mobile　robot.