Fully-hydrated concrete not involved in any reaction has been observed to exhibit aging creep. Both the solidification theory and the dissolution-precipitation theory are incapable of predicting such a behaviour. The microprestress theory proposed for this purpose is based upon an ambiguous physical mechanism. In this paper, a constitutive model motivated by Drozdov's adaptive link mechanism has been proposed. The model is capable of predicting aging creep, recovery and relaxation for linear elastic concrete subjected to diverse load histories and temperatures. The theoretical significance of the proposed aging Maxwell model has been critically evaluated.