We present the theory of a method to slow a linearly polarized probe pulse as it propagates through a duplicated two-level system driven by an orthogonally polarized control field. The method makes use of Zeeman coherence oscillations that arise in the atomic system because of the spatial and temporal modulation of the total polarization. This method exhibits properties similar to those that rely on electromagnetically induced transparency but without the existence of any trapping dark state. We demonstrate also the propagation of a polariton in the medium.