A comprehensive theoretical investigation of multiple slip in axially tensile-loaded f.c.c. crystals in n-fold symmetry positions (n = 4, 6, 8) is presented. The analysis is complete to second order in terms of series expansions of all variables in the prescribed small load increment. In the first part of the paper, general kinematic relations and slip-system inequalities are given, and several new results discovered that apply independently of hardening rule and degree of symmetry. Subsequent sections contain extensive first- and second-order analyses corresponding to four specific hardening theories, including Taylor's classical isotropic rule and the `simple theory' of anisotropic latent hardening. For minimum work, unifying relations are found connecting a generic hardening parameter, its rate of change with load, and the first and second derivatives of axial stretch that hold for all four theories.