  Functional equations with one catalytic appear in several combinatorial
applications, most notably in the enumeration of lattice paths and in the
enumeration of planar maps. The main purpose of this paper is to show that
under certain positivity assumptions the dominant singularity of the solutions
have a universal behavior. We have to distinguish between linear catalytic
equations, where a dominating square root singularity appears, and non-linear
catalytic equations, where we - usually - have a singularity of type 3/2.
