This paper describes a novel approach to dynamical modeling of asymmetries in electric machines and polyphase systems (e.g., the ones caused by unbalanced supply waveforms). The proposed technique is a polyphase generalization of the dynamic phasor approach from power electronics and electric drives. The technique is applicable to nonlinear models, and offers distinct advantages in modeling, simulation and control with respect to standard time-domain models. In a steady-state, the dynamic phasors reduce to standard phasors from ac circuit theory. We performed experiments and simulations involving a three-phase induction motor and a three-phase synchronous permanent magnet motor, and we demonstrate that models based on dynamic phasors provide very accurate descriptions of observed transients. In a steady state, our approach yields improved equivalent circuits that contain coupling between the positive and negative sequence subcircuits.