  The fermion propagators in the fivebrane background of type II superstring
theories are calculated. The propagator can be obtained by explicitly
evaluating the transition amplitude between two specific NS-R boundary states
by the propagator operator in the non-trivial world-sheet conformal field
theory for the fivebrane background. The propagator in the field theory limit
can be obtained by using point boundary states. We can explicitly investigate
the lowest lying fermion states propagating in the non-trivial ten-dimensional
space-time of the fivebrane background: M^6 x W_k^(4), where W_k^(4) is the
group manifold of SU(2)_k x U(1). The half of the original supersymmetry is
spontaneously broken, and the space-time Lorentz symmetry SO(9,1) reduces to
SO(5,1) in SO(5,1) x SO(4) \subset SO(9,1) by the fivebrane background. We find
that there are no propagations of SO(4) (local Lorentz) spinor fields, which is
consistent with the arguments on the fermion zero-modes in the fivebrane
background of low-energy type II supergravity theories.
