  As was observed by Grigoriev and Tseytlin, the Pohlmeyer-reduced AdS_2 x S^2
superstring theory possesses N=(2,2) worldsheet supersymmetry. We show, at the
classical level, that the AdS_3 x S^3 and AdS_5 x S^5 superstring theories in
the Pohlmeyer-reduced form reveal hidden N=(4,4) and N=(8,8) worldsheet
supersymmetries. Our consideration is based on the modified mass-deformed
gauged WZW action for the superstring equations. We present the explicit form
of the supersymmetry transformations for both the off-shell action and the
superstring equations. The characteristic feature of these transformations is
the presence of non-local terms.
