Most natural deformations are variable in intensity throughout a given region. If the variations are evenly distributed and sufficiently numerous, it is useful to consider a measure of average strain for the region. In this paper, the average deformation and average strain for a region are defined in terms of the local deformation gradients at each point. The definition is compatible with calculations based on the boundary shapes of the region before and after deformation. Using the average deformation as a threshold value, local variations are expressed as deviations from the average, i.e. perturbations. It is demonstrated that the perturbations are independent of the regional strain and that their mathematical form is limited by certain constraints.If the perturbations have the form of straight-sided bands, it is shown that they must result from a differential simple shear, a differential simple shortening, or combinations of these. This distinction forms the basis of a classification proposed for banded perturbations: those formed by simple shear are S-bands; those by simple extension, P-bands; those by combined action, PS-bands. Many natural structures resulting from deformation in rocks (e.g. kinks, pressure-solution seams, shear zones, similar folds) are band-like in form and can be classified as above.