Abstract: Theoretical study of the time-varying mesh stiffness is critical to geared system dynamics.For spiral bevel gears at high speed and heavy load in aero-engines,a numerical solution was applied to investigate the compliance and stiffness for each instantaneous contact,based on the static deflections and directional forces obtained by TCA(tooth contact analysis) and LTCA(loaded tooth contact analysis).Analytical form for state transition matrix of parametrical excited system including periodically varying stiffness was derived from the assumption that the time-varying mesh stiffness is piece-wise linearity.By adjusting the pinion machine tool settings,different contact patterns,transmission error,contact ratio and mesh stiffness under the same load condition for a pair of spiral bevel gears were treated.The Floquet theorem was applied,therefore,a program to calculate the magnitudes of the characteristic multipliers was used to investigate the instability among the working rotation speed interval,based on a two-degree-of-freedom dynamic system.The influence of time-varying mesh stiffness on parametric vibration stability of the spiral bevel geared system was investigated.