  If G is a simple non-compact Lie group, with K its maximal compact subgroup,
such that K contains a one-dimensional center C, then the coset space G/K is an
Hermitian symmetric non-compact space. SL(2,R)/U(1) is the simplest example of
such a space. It is only when G/K is an Hermitian symmetric space that there
exists unitary discrete representations of G. We will here study string
theories defined as G/K', K'=K/C, WZNW models. We will establish unitarity for
such string theories for certain discrete representations. This proof
generalizes earlier results on SL(2,R), which is the simplest example of this
class of theories. We will also prove unitarity of G/K conformal field theories
generalizing results for SL(2,R)/U(1). We will show that the physical space of
states lie in the subspace of the G/K state space.
