The dynamic behavior of process models consisting of higher order sets of linear coupled hyperbolic partial differential equations is considered. The formalism of the Riemann representation of the solution to second order hyperbolic equations is extended to problems of any order. The general time domain solution can then be written in terms of integrals of disturbance functions weighted with generalized Riemann matrices. If the solution for the Riemann matrix is approximated, a common approximation method serves to obtain the complete solution for all state variables subject to all disturbances. The approach is demonstrated on two examples, a double pipe heat exchanger and a nonisothermal packed bed reactor.