Abstract
Two new models of three-dimensional anisotropic spiral self-avoiding walks are introduced with different types of spiral constraint. Series expansions for the two models are derived and analysed. One model is found to behave like the isotropic three-dimensional self-avoiding walk, while the other model appears to belong to a distinct universality class, with exponents nu approximately=0.655 and gamma approximately=1.24. It is argued that for these non-Markovian, undirected, unweighted walks, the absence of a plane of reflection symmetry in the allowed walks signals a new universality class.