This paper presents a back stepping solution of the periodic output regulation problem for general linear heterodirectional hyperbolic systems. By utilizing a time-varying signal model, regulators are determined for a general class of periodic reference inputs and disturbances. A systematic design procedure is developed for the state feedback regulator by solving the periodic regulator equations. In order to obtain an output feedback regulator, a time-varying finite-dimensional reference observer and a time-varying infinite-dimensional disturbance observer are determined. For this, a systematic back stepping approach is provided. The results of the paper are illustrated for a 4 x 4 hyperbolic system with periodic triangle reference inputs and sinusoidal disturbances subject to time-varying frequencies. (C) 2019 Elsevier Ltd. All rights reserved.