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We examine the effects of SU(3) breaking in the matrix elements of theflavour-diagonal axial currents between octet baryon states and find that SU(3)breaking may be substantial for some matrix elements. We estimate the strangeaxial matrix element in the proton to be between -0.35 and 0 and the matrixelement 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 $\Xi^-$ isdiscussed and its implications for nonleptonic weak processes discussed. Wealso estimate the matrix element of the axial current coupling to the $Z^0$between all octet baryon states. This may be important for neutrinointeractions in dense nuclear environments, where hyperons may play animportant role.Comment: 16 pages, 3 figures, late

SU(3) breaking in neutral current axial matrix elements and the spin content of the nucleon