In 1986, Osherson, Stob and Weinstein asked whether two variants of anomalous vacillatory learning, TxtFex* * and TxtFext* *, could be distinguished [3]. In both, a machine is permitted to vacillate between a finite number of hypotheses and to make a finite number of errors. TxtFext* *-learning requires that hypotheses output infinitely often must describe the same finite variant of the correct set, while TxtFex* *-learning permits the learner to vacillate between finitely many different finite variants of the correct set. In this paper we show that TxtFex* * ≠ TxtFext* *, thereby answering the question posed by Osherson, et al. We prove this in a strong way by exhibiting a family in TxtFex* 2 TxtFext* *.