In Marcus (1980), deterministic parsers were introduced. These are parsers which satisfy the conditions of Marcus's determinism hypothesis, i.e., they are strongly deterministic in the sense that they do not simulate non determinism in any way. In later work (Marcus et al. 1983) these parsers were modified to construct descriptions of trees rather than the trees them selves. The resulting D-theory parsers, by working with these descriptions, are capable of capturing a certain amount of ambiguity in the structures they build. In this context, it is not clear what it means for a parser to meet the conditions of the determinism hypothesis. The object of this work is to clarify this and other issues pertaining to D-theory parsers and to provide a framework within which these issues can be examined formally. Thus we have a very narrow scope. We make no ar guments about the linguistic issues D-theory parsers are meant to address, their relation to other parsing formalisms or the notion of determinism in general. Rather we focus on issues internal to D-theory parsers themselves.