Along most particle paths in polar ice sheets, ice experiences a slowly changing local deviatoric-stress pattern, and develops a fabric characteristic of its current stress state, in which there is generally a correspondence between non-zero strain-rate components and non-zero deviatoric-stress components. Where the stress pattern changes rapidly in special transition zones, fabric may evolve more slowly than the local stress field, and unusual or unexpected deformation patterns can result. The degree to which fabric tracks the local stress is determined by the relative characteristic times for changes in stress, given by the transition-zone width and ice velocity, and for changes in crystal orientation, given, in the absence of recrystallization, by the inverse of the local strain rate due to the principal stress. Recrystallization can significantly reduce the time-scale of fabric adjustment. We examine transition zones where ice (a) enters ice-stream margins, (b) is overrun by a migrating divide, and (c) flows through a strong saddle. Stress and fabric tend to be significantly misaligned in ice-stream margins and in flow through a saddle. When stresses that are markedly different from in situ stresses are applied to ice specimens during creep tests, deformation may be difficult to interpret.