T HE TENDANCY of a crack to extend under applied loads is governed by the cohesive forces acting near the crack tip. The crack-extension criteria of Griffith and Barenblatt take account of the cohesive forces in rather different ways, but are both of the same form. Therefore, if they are to agree, the surface energy T appearing in the Griffith criterion must be related in a definite way to Barenblatt's modulus of cohesion K. It is shown in this paper, from a detailed consideration of the cohesive forces, that the required relationship holds, in an asymptotic sense, if the forces act only over a short range; this is true in practice. Extension of the analysis to uniformly moving cracks then shows that K is a function of velocity, even for a perfectly elastic-brittle body. This has not been noted previously. Finally, the relative advantages of the two formulations are compared.