This article is devoted to the Cauchy problem for nonhomogenous nonstrictly hyperbolic first order systems of differential equations with two independent variables. Unlike strictly hyperbolic systems, the real roots of the characteristic equation can be multiples for them. This leads to a coincidence of characteristics, which affects the formulation of the Cauchy problem. We use a geometric approach to this problem, which is based on representing such systems as pairs of differential 2-forms on a four-dimensional space. To find caustics of solutions, we use methods of singularity theory instead of Radon’s lemma.