A nondeterministic operation is characterized by the fact that its application to a given set of parameters can yield any one of several possible outcomes. This paper discusses ways to specify, implement, and reason about nondeterministic operations in the context of abstract (algebraic) data types. The notion of an implementation of a data type that includes nondeterministic operations is formalized, and the criteria for judging the "correctness" of such implementations are specified. The formalism developed allows implementations of nondeterministic operations to embody varying degrees of the full extent of nondeterminism allowed by the semantics of a type; in particular, deterministic implementations of nondeterministic operations are allowed.