The uniaxial compression-creep behavior of unidirectionally reinforced continuous-fiber composite materials was investigated for the case where both the matrix and the fiber underwent plastic deformation by creep. The creep behavior of NiAl composites reinforced with 5 to 20 vol pct tungsten fibers was characterized at 1025 ЊC. The NiAl-W composites exhibited a three-stage creep behavior, with distinct primary, secondary, and tertiary creep. Microstructurally, tertiary creep was characterized by one of the following fiber-deformation mechanisms: brooming, bulging, buckling, or kinking. The composite tertiary creep is modeled by solving for global or local kink-band evolution, with composite deformation contributing, respectively, to fiber buckling or kinking. The model predicts (1) the critical strain for the onset of the tertiary stage to be most sensitive to the initial kink angles, while being relatively insensitive to the initial kink-band heights and (2) the critical strain to vary inversely with the volume fraction of fiber in the composite. Reasonable agreement between model predictions and experiments is obtained.