  Using numerical diagonalization techniques, we explore the effect of local
and bond disorder on the finite temperature spin and thermal conductivities of
the one dimensional anisotropic spin-1/2 Heisenberg model. High-temperature
results for local disorder show that the dc conductivties are finite, apart
from the uncorrelated - XY case - where dc transport vanishes. Moreover, at
strong disorder, we find finite dc conductivities at all temperatures $T$,
except T=0. The low frequency conductivities are characterized by a nonanalytic
cusp shape. Similar behavior is found for bond disorder.
