The extension of the continental lithosphere is considered in terms of the deformation of a thin viscous sheet with a temperature-dependent rheology which is governed primarily by the strength of the upper mantle. The lithosphere is subjected either to a constant strain rate or to a strain-rate decreasing with time, corresponding to the stretching of a region of fixed volume with a constant velocity boundary condition. The progress of the extension is influenced by the decrease in strength of the lithosphere, owing to its attenuation, and by an increase in strength resulting from cooling. The relative importance of these two effects depends on two parameters, a dimensionless strain rate and the total strain. For a given strain rate the extending lithosphere goes through two phases as the strain increases: in the first, the effect of thinning the lithosphere is predominant and the average strength of the lithosphere remains close to, and perhaps slightly below, its original strength: in the second, the effect of cooling of the lithosphere leads to very rapid increase in strength as a function of strain, resulting, presumably, in an effective limit on the degree of stretching that the lithosphere experiences. For the case of strain rate decreasing with time, when the initial strain rates are of order 10-15 s-1, this maximum extension is between 100% and 150%; for a strain rate of 10-14 s-1 the maximum lies around 400% to 500%. At higher strain rates than this, very large extension may occur before cooling significantly affects the strength of the lithosphere. This model accords well with the constraints available from the continental margins of the North Atlantic.