We present an extension of the classical testing semantics for the case when nondeterminism is unbounded. We define the corresponding may and must preorders in the new framework. As in the bounded setting the may preorder can be characterized by using the set of finite traces of processes. On the contrary, in order to characterize the must preorder is necessary to record some additional information about the infinite behavior of processes. This characterization will be an extension of acceptance sets, considering not only the finite traces a process can execute but also its infinite traces. Keywords: Process algebra, CSP, unbounded nondeterminism, operational semantics, testing semantics.
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