In　this　paper,　we　analyze　the　transverse　nonlinear　vibration　of　a　rotating　flexible　disk　with　a　periodically　varying　rotating　speed,　subjected　to　a　rotating　point　force.　Based　on　a　small-stretch,　moderate-rotation　flexible　disk　theory　of　the　Nowinski　and　the　von　Karman　type　field　equations,　the　nonlinear　governing　equations　of　motion　are　derived　for　the　rotating　flexible　disk,　which　are　coupled　equations　among　the　radial,　tangential　and　transverse　displacements.　According　to　the　Galerkin　approach,　a　four-degree-of-freedom　nonlinear　system　governing　the　weakly　split　resonant　modes　are　derived.　The　resonant　case　considered　here　is　1:　1:2:2　internal　resonance　and　a　critical　speed　resonance.　The　primary　parametric　resonance　for　the　first-order　sin　and　cos　modes　and　the　fundamental　parametric　resonance　for　the　second-order　sin　and　cos　modes　are　also　considered.　The　method　of　multiple　scales　is　used　to　obtain　a　set　of　eight-dimensional　nonlinear　averaged　equations.　Based　on　the　averaged　equations,　the　stabilities　of　the　steady　state　nonlinear　responses　are　analyzed.　Using　numerical　simulations,　the　influence　of　different　parameters　on　the　nonlinear　vibrations　of　the　spinning　disk　is　detected.　It　is　concluded　that　there　exist　complicated　nonlinear　behaviors　including　multi-pulse　type　chaotic　motions,　periodic　and　period-n　motions　for　the　spinning　disk　with　a　varying　rotating　speed.　It　is　also　found　that　among　all　parameters　the　damping　and　excitation　have　important　influence　on　the　nonlinear　responses　of　the　spinning　disk　with　a　varying　rotating　speed.