There are described some algebraic structures on a space of belief functions on a two-element frame, namely so called Dempster's semigroup (with Dempster's operation ⊕), dempsteroids, and their basic properties. The present paper is devoted to the investigation of automorphisms of Dempster's semigroup. Full characterization of general and ordered automorphisms is obtained, their parametric description is stated both in intuitive and explicit forms. There is also full characterization of ordered endomorphisms, and other related results.