Abstract: Based on the homogenization theory , the multi-scale analysis methods of the viscoelastic property , and theeffective thermal stress relaxation laws are studied. By defining the concepts , the effective thermal stress relaxation modulus ( ETSRM) and the effective time-dependent coefficients of thermal expansion ( ETCTE) , the thermal viscoelastic constitutive equation is expressed in the same form as that of conventional materials. Besides , a homogenization-based methodfor predicting the effective viscoelastic relaxation modulus , ETSRM and ETCET is given. It is pointed out that , for viscoelastic composite materials , the thermal expansion coefficients are time-dependent , and the thermal expansion processcan not be completed instantaneously , exhibiting an obvious time-delay effect . The analysis of several kinds of specialcomposite materials shows that : (1) The thermal expansion of porous material has an instantaneous character , its ETCTEis the same as that of the matrix material which is time-independent , and its thermal stress relaxation law is also the sameas that of the matrix material ; (2) For a special kind of composite materials of which the relaxation moduli of all the components can be expressed as the products of different individual time-independent coefficients and a same time-dependentfunction , the effective time-dependent thermal expansion coefficient is time-independent , and the character of the relaxation laws is the same as that of conventional materials.