The Abelian and non-Abelian gauge potentials Auv are known to describe chiral fields. Here we study their interactions with dual extended objects. The region occupied by these objects is shown to behave like a distinct phase of chiral fields which is nondissipative under suitable geometric conditions. A method for the realization of the 't Hooft algebra in these systems is outlined. The concept of electric and magnetic duality in electromagnetism is generalized to chiral fields with values in a symmetric space.