A theory for the dynamic electrophoretic mobility mu of spherical colloidal particles in concentrated suspensions in an oscillating electric field is proposed on the basis of Kuwabara's cell model. The dynamic mobility depends on the frequency omega of the applied electric field and the particle volume fraction phi as well as on the reduced particle radius kappa a (where kappa is the Debye-Huckel parameter and a is the particle radius) and the zeta potential zeta. A mobility formula which involves numerical integration is obtained for particles with zero permittivity and low zeta. It is found that the mobility magnitude decreases with decreasing kappa a as in the static case (omega = 0) and as in the single particle case (phi --> 0) and that it decreases with increasing omega as in the single particle case. However, the phi dependence of the mobility magnitude is much more complicated. Namely, for small kappa a the mobility magnitude decreases with increasing phi as in the static case. For large kappa a it increases with increasing phi. For moderate kappa a and not very low omega the mobility magnitude may exhibit a maximum. In all cases the omega dependence of the mobility magnitude becomes less as phi increases, that is, the dynamic mobility at any omega approaches the static mobility as phi increases. An accurate mobility formula without involving numerical integration applicable for all kappa a at zero particle permittivity and low zeta is also derived. This formula is applicable even for high zeta at kappa a --> infinity unless the dynamic relaxation effect becomes appreciable.