Cytokinesis in animal cells is accomplished by the active constriction of the equatorial regions of a cell by an actomyosin‐containing contractile ring. The mitotic apparatus specifies the position and orientation of the furrow such that the mitotic spindle is always bisected. Global cortical contractions occur in the cortex of a cell prior to cytokinesis that are independent of the presence of the mitotic apparatus. It was proposed some years ago that the asters of the mitotic apparatus could act to relax (...) the preformed cortical tension in their vicinity. This would produce a differential in tension between the equatorial regions and the adjacent regions of the cortex so that the equatorial regions would contract, forming a cleavage furrow. It can be shown that, as it stands, this theory cannot explain cleavage. However, if cortical contractile elements are assumed to be laterally mobile in the plane of the cortex, then the astral relaxation theory can account for many of the aspects of cleavage, including the formation of the contractile ring. Similar schemes may account for the behaviour of the lamellapodia of motile cells. (shrink)