  In many theories with flat directions of scalar potential, static vortex
solutions do not exist for a generic choice of vacuum. In two Euclidean
dimensions, we find their substitutes --- constrained instantons consisting of
compact core formed by Abrikosov--Nielsen--Olesen vortex and long-ranged cloud
of modulus field. In (3+1) dimensions, an initial compact configuration of
string topology evolves in such a way that at every point in space the modulus
relaxes, in a universal manner, to one and the same value characteristic to the
theory.
