  We examine the effects of SU(3) breaking in the matrix elements of the
flavour-diagonal axial currents between octet baryon states and find that SU(3)
breaking may be substantial for some matrix elements. We estimate the strange
axial matrix element in the proton to be between -0.35 and 0 and the matrix
element of the flavour-singlet current in the proton to be between -0.1 and
+0.3 from the E-143 measurement g_1(x) . The up-quark content of the $\Xi^-$ is
discussed and its implications for nonleptonic weak processes discussed. We
also estimate the matrix element of the axial current coupling to the $Z^0$
between all octet baryon states. This may be important for neutrino
interactions in dense nuclear environments, where hyperons may play an
important role.
