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Canonical aberration theory has been applied to analyze the aberration structure of both electrostatic and magnetic multipoles. It is shown rigorously that for 2N‐pole magnetic multipoles with N=even, there is no axially symmetric aberration of any order, while for all the other cases of electromagnetic multipoles, there is always an axially symmetric aberration of the order of 2N-3. The method used is general in nature and can be applied to obtain detailed formulas of higher‐order aberrations of multipoles and also to study their off‐axis aberrations.