  Thom (residual) polynomials in characteristic classes are used in the
analysis of geometry of functional spaces. They serve as a tool in description
of classes Poincar\'e dual to subvarieties of functions of prescribed types. We
give explicit universal expressions for residual polynomials in spaces of
functions on complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These expressions
lead to a partial explicit description of a stratification of Hurwitz spaces.
