Recent works have paved the way to theoretical predictions of the conditions governing the transition from internal to external oxidation of metals and alloys: such conditions directly result from Wagner (1959)'s classical analytical model, provided that it is made to incorporate a heuristic decrease of diffusion coefficients upon the fraction of oxides, aimed at representing their "barrier effect" upon diffusion. The aim of this paper is to extend these works by removing some of the very restrictive hypotheses introduced by Wagner (1959). First, the formulation initially limited to small fractions of oxides is extended to arbitrarily large fractions. Even in their modified form, the equations are still solvable entirely analytically, albeit with a change of the predicted value of the "critical" fraction of oxides, above which internal oxidation must give way to external oxidation. The new value is in better agreement than previous ones with the scarce available experimental estimates. Second, the formulation is extended to finite-instead of infinitesimal-values of the solubility product governing local chemical equilibrium between the oxide and the chemical elements dissolved in the metallic matrix. The nonlinear equations of the diffusion/precipitation problem then become much more complex and amenable only to some hybrid analytical/numerical solution. The results, although interesting, raise a number of issues essentially tied to the basic hypothesis made of instantaneous local thermodynamic equilibrium. It is finally shown, using a simplistic, prototype kinetic model of oxide precipitation, that relaxation of this hypothesis should permit to solve at least some of these issues.