A general theory of multipactor in orthogonal electric and magnetic fields is given. The model consists of two parallel plates of known secondary emission properties, across which a time varying voltage is applied, and between which a constant magnetic field is applied. Expressions are derived for the resonant phases at which the RF-driven cascades occur; these reduce to previously derived expressions in the limit of the vanishing magnetic field. In addition, this work obtains the conditions governing the stability of the motion about those phases, as well as a dynamic constraint from imposing the restriction that each impact on a plate is the first impact that is allowed by the equations of motion. Chaotic effects from the random ejection velocities of the secondaries are addressed for the first time. It is proven that the phase focusing effect from the radio frequency (RF) interaction will overcome the dispersive effect from the random emission, provided that the mean square emission velocity is sufficiently small; in that case stability of the multipactor is determined by the stability of an ‘‘ideal’’ multipactor with zero emission velocity. That reduces the multipactor parameter space to only two control parameters: the normalized RF electric and DC magnetic field strengths. The multipactor prone region is mapped over the entire parameter space by applying both dynamic and secondary yield criteria; previous studies have been limited to specific cases. Finally a simplified model is adopted to address collective effects and multipactor saturation from the space charge buildup. In addition to the mutual electron repulsion, we find that the previously neglected interaction of the electron sheath with the induced image charge on the plates is important to saturation.