Formulas are presented for the maximum energy gain per turn of ions in a fixed-frequency cyclotron with three identical dees symmetrically spaced. Calculations have been made for dees of general angle θ and specific angles 60°, 90°, and 120°. Dee excitations in which the dee voltages are all in phase or phased at 120° with respect to each other have been considered. The type of ions that can be accelerated is dependent upon the mode of excitation. In a 60° three-dee cyclotron with variable rf phasing, protons, deuterons, and tritons can be accelerated in the nonrelativistic energy region at substantially the same magnetic field and oscillator frequency. A 20-inch cyclotron of this type has been operated successfully.