In this paper the behaviour of descent methods for minimization of functionals, which are in effect strong and bounded convex except in the neighbourhood of the singularity of the gradient is investigated. Sufficient and necessary conditions of convergence and assertions about the convergence speed in the neighbourhood of the singularity are stated independence of parameters of the descent methods. In general, in the “drainage area” of the minimum the convergence of the Kuhn-Algorithm for solving the Fermat-Problem may be proved with this means.