We investigated the thermal stability of strained layers of InGaAs and InAlAs on InP. Epilayer and interface quality was assessed by high-resolution x-ray diffraction and electron mobility measurements as a function of annealing cycle. Both techniques show that pseudomorphic heterostructures retain their high crystalline quality at annealing temperatures of up to 700-800-degrees-C, despite exceeding the Matthews-Blakeslee [J. Cryst. Growth 27, 118 (1974)] critical layer thickness by as much as a factor of 4-8. On the other hand, layers which are partially relaxed (incoherent) as-grown relax further during annealing. These findings demonstrate that layers which are beyond the predicted critical thickness, but coherently strained after growth, are stable to normal device processing and operating temperatures and hence may be suitable for use in device heterostructures.