  We study vortex solutions in a theory with dynamics governed by two weakly
coupled Abelian Higgs models, describing a hidden sector and a visible sector.
We analyze the radial dependence of the axially symmetric solutions constructed
numerically and discuss the stability of vortex configurations for different
values of the model parameters, studying in detail vortex decay into lower
energy configurations. We find that even in a weak coupling regime vortex
solutions strongly depend on the parameters of both the visible and hidden
sectors. We also discuss on qualitative grounds possible implications of the
existence of a hidden sector in connection with superconductivity.
