In　this　paper,　we　analyze　the　transverse　nonlinear　vibration　of　a　rotating,　flexible　disc　with　a　periodically　variational　rotating　speed,　subjected　to　a　rotating　point　force.　Based　on　a　small-stretch,　moderate-rotation　plate　theory　of　Nowinski　and　von　Karman-type　plate　equation,　nonlinear　governing　equations　of　motion　for　the　spinning　disk　are　derived,　which　are　a　set　of　the　coupled　equations　among　the　radial,　tangential　and　transverse　displacements.　According　to　the　Galerkin　approach,　a　set　of　four-degree-of-freedom　ordinary　differential　equations　is　derived.　The　resonance　case　considered　here　is　1:1:2:2　internal　resonance,　a　critical　speed　resonance　and　principal　parametric　resonance.　The　method　of　multiple　scales　is　used　to　obtain　eight-dimensional　nonlinear　averaged　equations.　The　influence　of　different　parameters　on　the　nonlinear　vibrations　of　the　spinning　disk　is　detected.　It　is　concluded　that　there　exist　complex　nonlinear　behaviors,　which　include　the　multi-pulse　type　chaotic　motion,　periodic　and　period-nmotion　in　the　spinning　disk　system.　We　also　find　that　among　all　these　parameters　those　relative　to　the　damping　and　excitation　are　more　important.