In this paper, the time-dependent damage and fracture of fiber-reinforced ceramic-matrix composites (CMCs) are investigated considering fiber oxidation and fracture at an elevated temperature. The shear-lag model combined with the fiber/matrix interface oxidation model, the interface debonding criterion, fiber strength degradation model and fiber failure model is adopted to analyze the microstress field in the damaged composite. The relationships between the first steady-state matrix cracking stress, composite tensile strength, fiber/matrix interface debonding and sliding, oxidation temperature and oxidation time are established. The effects of fiber volume fraction, fiber/matrix interface shear stress, fiber strength and oxidation temperature on the evolution of first steady-state matrix cracking stress and composite tensile strength versus the oxidation time are analyzed. The first steady-state matrix cracking stress and composite tensile strength of 2D C/SiC and 2D C/[SiC-B4C] composites after oxidation at 700 degrees C, 1200 degrees C and 1300 degrees C in air atmosphere are predicted for different oxidation time.