For an arbitrary function F defined on the group of homotopy classes of mappings of a finite polyhedron X to the circle and taking values in an Abelian group Q, the notion of order is defined. The order ord F is compared with the algebraic degree of F. It is proved that ord F Sj deg F and deg F Sj dim X ord F. The inequality ord F -4 deg F is proved in the case where Q is torsion-free or ord F 1.