Curve face gear pair and noncircular bevel gear pair are collectively referred to as spatial noncircular gear pair (SNCGP). Different from the traditional gear transmission with fixed shafts, spatial noncircular gear (SNCG) compound transmission can realize compound motion with variable transmission ratio between intersecting axes, and has a broad engineering application prospect. It includes two categories named speed reduction and speed increase. Based on the gear meshing theory, screw theory and calculus, a screw analysis method of SNCG compound transmission was proposed, which directly and comprehensively reflected the compound motion characteristics of rotation and axial movement. Firstly, a unified coordinate system was established. The screw geometric characteristics of compound motion were discussed, including instant screw axis, axode, pitch surface and its normal equidistant surface. The screw principle of compound motion was revealed. Then, according to this method, combined with the motion process of generator with different tooth profiles, the tooth surface of each SNCG was obtained. Finally, gear machining, tooth surface measurement, transmission ratio measurement and axial displacement measurement were carried out, which verified the correctness of this screw analysis method for SNCG compound transmission, and laid a foundation for further study and application.