The inelastic response of fiber-reinforced ceramic and metal matrix composites under fixed load at elevated temperature is due to the complementary effects of creep and damage in the constituents. After matrix cracking or tensile creep relaxation in a short time, subsequent deformation and failure are driven by shear stress relaxation in the matrix and at the fiber-matrix interface around broken fibers. The shear creep causes stress redistribution to unfailed fibers, causing Further fiber breakage and shear relaxation, culminating in abrupt failure of the composite. This sequence of events is modeled both analytically and numerically within the Global Load Sharing (GLS) approximation previously utilized for quasi-static loading. Analytically, a unit cell model is used to obtain simple closed-form relationships For the time-dependent relaxation of the shear at the interface. This relaxing shear stress is then incorporated into a simulation model which follows the evolution of slip and fiber damage up to failure. The slip lengths and failure times are predicted vs matrix creep exponent n, fiber Weibull modulus in, applied load and, interestingly, physical specimen length. An analytic model for failure shows good agreement with the simulation results and so can be used for qualitative estimates of lifetime. Application to Ti-MMCs is discussed. (C) 1997 Acta Metallurgica Inc.