The model we advanced in a previous paper about DNA circularization (J. Phys. Chem. 1996, 100, 9968-9976), is extended to the sequence-dependent equilibrium between relaxed and supercoiled forms of circular DNAs. In the framework of first-order elasticity, we evaluate the canonical ensemble partition function and the related thermodynamic properties in terms of continuous variations of writhing and linking numbers, giving an estimate of the writhe transitions. The comparison with the Monte Carlo results is very significant. It convincingly proves the validity of the proposed model as a favorable alternative to computationally heavy Monte Carlo simulations. Moreover the model is suitable to study the sequence-dependent effects in the writhe transitions and offers good perspectives for further developments.