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The privileged field of classical algebra and term-rewriting systems is that of strictly deterministic systems: the conjhence property is generally assumed to hold, which implies determinism for the result of the computations, even if there exist several different computation paths. In this paper, we introduce a bounded nondeterministic choice operator "u" into algebraic specifications and related term-rewriting systems. The operator "u", which constructs sets of values, satisfies ACdoi:10.1016/0304-3975(86)90005-8 fatcat:vbzjnh7lnvfulni4xwag7g7tu4