Summary: Algebraic specifications are generalized to the case of nondeterministic operations by admitting models with set-valued functions (multialgebras). General (in particular, nonconfluent) term-rewriting systems are studied as a specification language for this semantic framework. A calculus for nondeterministic specifications is given which is similar to term rewriting but which employs an additional determinacy predicate. Soundness, ground completeness, and initiality results are given. Small examples illustrate the range of possible applications.