Fatigue damage growth can be described by the gradual reduction of the stiffness and strength, and damage expressed by the two degradation methods are equivalent. According this assumption, a pair of cumulative fatigue damage models based on residual stiffness and residual strength is proposed, and then the connection between the two damage indices is established. The two damage models follow equation with the same form, but the parameters in them are not equal. Each of the two models contains three unknown parameters which have pertinent effect on the damage growth rates, in addition, the models also take into account of the effects of stress levels and stress ratios. By fitting the experimental data, it is observed that the parameters in damage functions obey the linear relation well, and the unknown constants are deduced with finite tests easily. Finally, the models are found to give a good description of fatigue damage evolutions of different stacking sequence for both of the stiffness and strength.