The principles governing the oscillations in a klystron may be divided into four groups: (1) those of space resonance within each rhumbatron, previously discussed by Hansen; (2) the equations of coupled circuits, with modifications appropriate to space‐resonant systems; (3) the kinematics and dynamics of cathode‐ray bunching, previously discussed by the author; (4) the constraint on phase relations between the rhumbatrons introduced by the cathode‐ray bunches. It is shown here that (4) makes the oscillations assume forms very different from those familiar in free oscillations. These forms are described by general equations and then these equations are applied to three specific problems: maximizing the power output from an oscillator, minimizing the power input for an ideal regenerative amplifier, and finding how stable the frequency is against changes in cathode potential.