Harmonic (Fourier) analysis provides a series of multivariate descriptors that exactly quantifies the shapes of cephalopod suture patterns in the Subclasses Nautiloidea and Bactritoidea, and in four of the eight orders of the Ammonoidea. The method allows the calculation and graphic display of the mean suture patterns of the subclasses and orders studied, and exactly measures the morphological differences between groups. Discriminant analysis provides significant differentiation of the four ammonoid orders using only the harmonic amplitudes of the sutures. Discriminant analysis also indicates significant differences between the two symmetric halves of sutures in Acanthoclymenia neapolitana, and thereby measures the withingenotype norm of reaction in that species. Twelve sutural harmonic amplitudes are significantly correlated with ontogenetic changes in apertural size and shape in Koenenites cooperi. Specific harmonic amplitudes increase monotonically in the ontogeny of K. cooperi, but do not change within the phylogeny of its family, the Gephuroceratidae. This method permits statistical testing of assumptions of heterochronous evolution in cephalopod lineages.