In this paper we propose a mechanism for the ubiquitously observed, but essentially still unexplained, phenomenon of banding in sheared polymeric liquid crystals. In the course of it numerous analogies are brought in from other fields and a new rheological observation made on two lyotropic systems is announced and its relevance to banding discussed. The proposed explanation rests on two separate tenets. First, that buckling of uniaxially oriented birefringent fibrous entities accounts for the observed banding. Second, that the usually observed orientation relaxation after shearing (with which banding is usually associated) points to the existence of restoring forces which are extraneous to liquid crystals per se. These, we propose, are due to an elastic network which is part of the total system, but does not belong to its liquid crystal component and, as observed, is characteristic of polymer liquid crystals alone. These restoring forces can therefore provide the axial compression which produces the buckling. Amongst the numerous features quoted, special emphasis is given to the ''self extension'' phenomena which, if constrained, can be a strong contributing factor to (or even the cause of) the buckling, and thus band formation. The unusual rheological effect in the hydroxypropylcellulose-water system, the spontaneous stress build-up on the cessation of shear, while being a notable phenomenon in its own right, is discussed here because of its observed limitation of the banding process.