  We generalize the notion of Thom polynomials from singularities of maps
between two complex manifolds to invariant cones in representations, and
collections of vector bundles. We prove that the generalized Thom polynomials,
expanded in the products of Schur functions of the bundles, have nonnegative
coefficients. For classical Thom polynomials associated with maps of complex
manifolds, this gives an extension of our former result for stable
singularities to nonnecessary stable ones. We also discuss some related aspects
of Thom polynomials, which makes the article expository to some extent.
