We study the propagation of ultrashort pulses in x-ray waveguides (WGs) by addressing the problem of the temporal dispersion. Starting from basic equations, by means of numerical calculation we demonstrate that far from the absorption edges of the WGs the cladding's material dispersion is negligible. However, close to the absorption edge significant dispersion can take place. This behavior could in principle be exploited to manipulate incoming chirped beams. Moreover, using the two coherent beams produced by the WG in the second (and higher) order of resonance suggests the use of the WC as a dispersion-free beam splitter, which can facilitate x-ray pump-probe experiments in the femtosecond temporal range without the need for external sources.