We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2-theories. We show that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et al. – butfor the case of circular redexes , for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collectionand rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms.