The potential and electric field distributions in a traveling wave deflection system are derived for a sinusoidal deflecting signal. They are then generalized for application to arbitrary deflecting signals. It is shown that a longitudinal field exists and depends on the odd derivatives of the signal. This component of the field modulates the velocity of the beam and gives rise to errors in focusing and time axis position. The velocity modulated beam is then dispersed by the time axis deflection system. The nonuniformity which must exist in the deflecting component of the field is shown to depend on the even derivatives of the deflecting signal. The nonuniformity gives rise to dispersion and errors in deflection of the beam by the traveling wave deflection system. Generalized expressions for these errors are derived, and the errors are evaluated for a representative set of conditions.