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Multi-axis electrical discharging machining (EDM) is the most commonly used manufacturing method for shrouded blisks. However, debris is difficult to be evacuated from a discharge gap, severely affecting the machining efficiency. Spatial planetary movements of a tool electrode can generate a non-uniform flow field in a discharge gap, promoting the evacuation of debris. This paper proposes a spatial planetary movement method for EDM of inclined holes. Screw theory is used to derive the kinematics of a spatial planetary movement, and the coordinate increments of each axis in an interpolation period can be calculated. The trajectories of the spatial planetary movements are simulated. The reliability of the method is confirmed by the simulation. Then, a multi-axis EDM machine can be controlled to drive a tool electrode to realize the spatial planetary movement. Machining experiments are carried out to explore the influences of the spatial planetary movement parameters on the machining performance of multi-axis EDM. Experiment results show that the increase in the amplitude of spatial planetary movements can improve discharge rate and gap status. The machining depth and machining efficiency of multi-axis EDM can be increased ulteriorly. And the speed of spatial planetary movements has no significant effect on the performance of multi-axis EDM. [ABSTRACT FROM AUTHOR]