A general formulation framework for an age-dependent constitutive equation of concrete is presented to account for the development of the elastic modulus at an early age. This is achieved by expanding the total stress vs. strain relation with respect to the time-varying elastic modulus. Two types of constitutive formulation frameworks are derived depending on whether (or not) the time-varying effect of the elastic modulus was taken into account in the linearized series expansion. The causes for the age-dependent deformations under sustained loads are defined in the formulation based on the two internal mechanisms of delayed elasticity and the ageing phenomenon. The ageing phenomenon is incorporated in a conventional delayed strain concept in terms of the variable elastic modulus with time. Four cases of age-dependent constitutive equations are formulated within the presented formulation framework by employing different types of creep models. The mechanical characteristics of the terms that comprise the various constitutive equations are examined and compared. Numerical application of the time-dependent test results of cylindrical specimens indicate that the creep formulation that considered the elastic modulus development showed a good agreement with the experimental result while the formulation that did not consider the elastic modulus development underestimated the result by 15%.