This paper considers the radial and vertical oscillations of a synchro‐cyclotron beam. It is found that various oscillations of substantially constant or increasing amplitude may occur in certain regions of the field, in which there are angular or other asymmetries, though only one possible oscillation (that atn≃⅕) can occur in a field that is cylindrically and vertically symmetric. The conditions for the various oscillations, and their behavior, are discussed.