Several regions with different governing failure mechanisms may be distinguished analyzing axial tension-tension cyclic loading of unidirectional (UD) composite. At high loads multiple fiber fracture takes place during the first loading cycle. The relative number of broken fibers depends on the maximum stress and can be estimated assuming that the fiber strength is a statistical property following Weibull distribution. Multiple fiber fracture (fragmentation) is possible because the load is transferred into the broken fiber through the interface. In cyclic loading with constant amplitude we usually assume that fibers do not experience fatigue and all fiber breaks occur during the first cycle. During the following cyclic loading debonds start to grow along the fiber/matrix interface and this is the main mode of damage progression analyzed in this paper. The extensive debonding reduces the load borne by the broken fiber causing new fiber breaks and connecting the multiple fiber breaks, finally leading to catastrophic rupture of the UD composite. Hence, understanding of the debond growth process in fatigue is crucial for fatigue life analysis in this load region.