This paper offers a generalized mechanical explanation for the origin and development of bandlike deformation structures such as shear zones, mylonite zones, kink bands, 'pressure-solution' seams, extension gashes, and similar folds.Methods of continuum mechanics are used to examine permissible variations in strain rate, stress, and rheological properties across a region containing ideal banded perturbations. For bands to develop, the rheological properties must vary across the banding. The physical basis for this variation is a corresponding variation in microstructure or chemical composition, influenced in turn by finite deformation, stress, and temperature. Many rocks are likely to soften or harden during progressive deformation and these changes may be enhanced by thermal or other agents. Deformation softening (including strain softening and rotation softening) is a cause of instability and has two effects: first, the deformation tends to accelerate under constant stress; second, the deformation tends to become locally perturbed. Deformation hardening has compensatory effects.Banded perturbations do not appear spontaneously in a deforming rock, but evolve towards an ideal banded form by processes of nucleation and propagation. Evidence for these processes comes from theoretical analysis, experimental data, and observation of bandlike structures that have formed as a result of natural processes of deformation.