Currently,　three　dimensions　topographic　measurement　for　gear　surface　is　becoming　the　research　focus.　However,　the　analysis　is　still　not　enough　on　theory　of　gear　surface　deviation.　Based　on　the　kinematic　principle,　the　degrees　of　freedom　(DOF)　of　gear　surface　are　analyzed　and　parameterized.　By　this　way,　the　gear　surface　is　illustrated　with　multi-degrees　of　freedom　(M-DOF).　The　gear　surface　deviations　are　separated　into　0th,　1st　and　high　order　deviations,　and　then　the　relationship　between　each　order　deviation　and　the　DOF　of　gear　surface　is　analyzed,　showing　that　the　gear　deviation　arised　from　the　unconstraint　DOF　of　gear　surface.　The　analysis　sets　up　the　theoretic　foundation　for　evaluation　of　gear　deviation.　An　evaluation　method　is　developed　for　gear　deviation　base　on　above　M-DOF　theory,　before　evaluation,　the　DOF　parameters　need　to　be　determined　by　orthogonal　distance　regression　and　then　the　corresponding　M-DOF　gear　surface　can　be　attained.　An　inspection　and　a　evaluation　are　carried　out　for　a　right　hand　helical　gear,　inspection　manners　used　include　characterized　curve　inspection　and　topographic　inspection,　results　of　evaluation　verify　the　validity　of　M-DOF　theory　for　gear　deviation　and　the　evaluation　method　based　on　M-DOF　regression　gear　surface,　providing　the　theory　foundation　and　technique　method　for　gear　holistic　quality　inspection.　©　2014　Journal　of　Mechanical　Engineering.