The misalignment of a gear coupling in a multirotor system is an important problem; itcan cause various faults. In the present work the non-linear coupled lateral torsionalvibration model of rotor-bearing-gear coupling system is developed based on theengagement conditions of gear couplings. Theoretical analysis shows that the forces andmoments acting on gear couplings due to the initial misalignment are from the inertia forcesof the sleeve and the internal damping between the meshing teeth, and depend on themisalignment, internal damping, the rotating speed, and the structural parameters of thegear coupling. Numerical analysis of the signature of vibration reveals that the even-integermultiples of the rotating speed of lateral vibration and the odd-integer multiples of thetorsional vibration occur in the misaligned system, and the integer multiples of vibration areapparent around the gear coupling.