  We investigate the modular properties of the characters which appear in the
partition functions of nonabelian fractional quantum Hall states. We first give
the annulus partition function for nonabelian FQH states formed by spinon and
holon (spinon-holon state). The degrees of freedom of spin are described by the
affine SU(2) Kac-Moody algebra at level $k$. The partition function and the
Hilbert space of the edge excitations decomposed differently according to
whether $k$ is even or odd. We then investigate the full modular properties of
the extended characters for nonabelian fractional quantum Hall states. We
explicitly verify the modular invariance of the annulus grand partition
functions for spinon-holon states, the Pfaffian state and the 331 states. This
enables one to extend the relation between the modular behavior and the
topological order to nonabelian cases. For the Haldane-Rezayi state, we find
that the extended characters do not form a representation of the modular group,
thus the modular invariance is broken.
