The failure of fiber reinforced composites at elevated temperatures can occur due to time-dependent degradation mechanisms of the constituent fibers, matrix, and/or interface. Here, analytic models are presented for predicting deformation and lifetime due to two important mechanisms of degradation when acting simultaneously. The mechanisms are matrix/interface creep and fiber degradation by slow crack growth within the fibers. Both mechanisms are non-linearly dependent on the state of stress in the material and so, when acting simultaneously over comparable time-scales, the damage rate is strongly accelerated due to the non-linear coupling of the mechanisms. The resulting composite lifetime can me much smaller than the life under conditions when only a single degradation mechanism is acting, even when the time scales of the two mechanisms differ by large amounts. For example, if when acting alone fiber degradation causes failure in time tf and creep causes failure in a time 100tf, when acting together the failure time can be 0.1tf or smaller at stresses on the order of 1/2 the ultimate fast-fracture strength. The remaining strength under single and combined degradation modes is also studied within these analytic models. Then, several “kinetic” laws for predicting the remaining strength versus time due to multiple degradation mechanisms, including the MRLife approach, are studied. Specifically, the individual remaining strengths for each degradation mode as found from the micro-mechanical models are used as input into the kinetic laws, and the predicted lifetimes are then compared to those from the micro-mechanical models to assess the accuracy of the kinetic laws.