Summary: The authors study in this article the Cauchy problem for partial differential equations of Fuchs type in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect other variables. The results are in some sense a generalization of those obtained in P. Pongérard and C. Wagschal [J. Math. Pures Appl., IX. Sér. 75, 409–418 (1996; Zbl 0858.35001)] for the non characteristic Cauchy problem in the space of entire functions and in P. Pongérard [J. Math. Sci., Tokyo 8, 89–105 (2001; Zbl 0984.35004)] in the case of Fuchsian operators.