  We consider a string theory based on an SU(1,1) Wess-Zumino-Novikov-Witten
model and an arbitrary unitary conformal fild theory. We show that the
solutions of the Virasoro conditions, in the unitarity regime of the SU(1,1)
theory, are states which lie in the Euclidean coset SU(1,1)/U(1). This shows
the validity, at the quantum level, of a time-like type of gauge in these
models.
