  In 1986, Osherson, Stob and Weinstein asked whether two variants of anomalous
vacillatory learning, TxtFex^*_* and TxtFext^*_*, could be distinguished. 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^*_* \neq TxtFext^*_*, thereby answering the question posed by
Osherson, \textit{et al}. We prove this in a strong way by exhibiting a family
in TxtFex^*_2 \setminus {TxtFext}^*_*.
