Abstract: Based on the analysis of the degree of cure and temperature dependent viscoelastic constitutive model of composite, the dimensionless parameters defined as De_m were proposed to characterize the viscoelasticity of composite in this paper. The parameters De_m can comprehensively reflect the effects of the degree of cure and temperature on the viscoelasticity of a composite during cure. When all of the values of De_m are higher than 10², the composite matrix is in a flow state. When all of the values of De_m are less than 10^-2, the composite is in an elastic state. Only when one or more De_m lie between 10² and 10^-2, the composite is in viscoelastic state. The behavior of the AS4 fiber/3501-6 polymer matrix composite was used as example, the development of the viscoelasticity of the composite was analyzed according to the evolution of the parameters De_m during the typical curing cycle. The result shows that the gelation time determined by the parameters De_m is consistent with that obtained by experimental tests. According to the effect of viscoelasticity of composite on the accumulation of residual stress, the analysis procedure on the residual stress was divided into the flow stage and the viscoelasticity stage, and the cure state dependent viscoelastic constitutive models were put forward. The proposed models were verified by comparing their predictions with those of the original constitutive model. The results show that the residual stresses predicted by the proposed models are consistent with those predicted by the original model, but the computing time and storage space required by the proposed models are greatly reduced.