We review our progress on the lattice calculation of low moments of both the unpolarised and polarised nucleon structure functions. (orig.)Talk presented by R. Horsley at the 29th symposium on the theory of elementary particles, Buckow (DE), 14 refs.Available from TIB Hannover: RA 2999(96-003) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman