This paper describes the damage process of a composite reinforced by plain woven glass cloth under O-tension fatigue loading. The study is summarized as follows. The fatigue process can be divided into three stages similarly to the case of multi-directional laminates. The initial stage is the stage where the modulus decreases rapidly. This rapid decay is caused by debondings in the weft and matrix cracks. Through the end of the initial stage to the beginning of second stage, the characteristic damage state is observed. This state should be called as the micro-CDS if compared with the CDS for multi-directional laminates. After the rapid modulus decay, debondings in the warp and micro-delaminations between weft and warp occur. In the second stage, the modulus decreases gradually mainly due to them. In a few cycles just before failure (final stage), it changes rapidly again. The concept of the 'Unit Cell' is proposed for understanding the damage of woven composites. It consists of one cross-over of weft and warp of the fabric. In the final stage, the damage of 'Unit Cell's is accelerated like chain reaction. For woven composites, the damage of each 'Unit Cell' and its distribution control the total fatigue damage of the material.