A micromechanical model is developed for the prediction of the growth rate of fatigue damage zones in unidirectional fibre composites subjected to cyclic tension-tension loading. The fatigue damage occurs by progressive fibre breaks caused by the debond crack tip stress fields of fibres that have broken in earlier load cycles. The debond crack tips are taken to advance along the broken fibres due to a cyclic slip-induced decrease in the frictional sliding shear stress acting along the debonded parts of the fibres that undergo repeated forward and reverse slip. The fatigue life is calculated as the number of load cycles for damage zones to reach a critical size where rapid composite failure can occur by longitudinal splitting cracks connecting damage zones within the specimen. A parameter study is performed to explore how the damage growth rate and fatigue life depend on microscale parameters (mechanical properties of fibre, matrix and fibre/matrix interface).