We prove by topological methods methods that in the context of SU(2) gauge theory the integers labelling the homotopy classes of Yang-Mills and Higgs fields are equal for periodic instanton and dyon configurations. A similar statement is true for the group SO(3) and, in the periodic instanton case, whenever a simply connected group is broken down to an abelian subgroup. We briefly discuss how the result goes over to the canonically quantized theory
