The problem of constructing fields from local observables is considered in the framework of a concrete algebraic theory with superselection rules proposed recently by V. N. Sushko and the author. The possibility of using the methods developed by Doplicher, Haag, and Roberts is discussed. A number of preliminary results in this direction is obtained: 1) the set of cyclic and separating vectors of the local observable algebras of coherent superselection sectors is described in detail; 2) physical equivalence of the coherent sectors is proved anda considerable number of criteria is deduced for the local unitary equivalence of the sectors; 3) a necessary condition for duality is found and the relation between the duality properties and local unitary equivalence is clarified.