Intermediate and deep focus earthquakes in Wadati-Benioff zones are thought to occur in the cold interiors of downgoing slabs which are significantly stronger than the warmer mantle. Given that earthquakes in oceanic lithosphere appear restricted by an isotherm, and hence a given value of lithospheric strength, we investigate whether a similar formulation is useful for subducting plates. Strength in downgoing slabs should be affected by both pressure and temperature, an effect previously treated using a depth-dependent limiting temperature for seismicity [Wortel, 1982>. We find this limiting temperature implies that a possible limiting strength increases strongly with depth, unless either the temperatures were too low or the activation volume too large. Comparison of the analytic model used by Wortel with numerical thermal models appears to exclude the first possibility. We explore the second possibility by using the numerical thermal model to compute strength contours for flow law constants reported from laboratory experiments, and find that the expected pressure strengthening is large enough that the slab should have considerable strength well below the deepest seismicity. We conclude that if laboratory results are applicable to these conditions, either a strongly depth-dependent limiting strength exists or factors in addition to strength control the distribution of subduction zone earthquakes. ¿ American Geophysical Union 1988