Two alternative interpretations of the equilibrium notion employed by Walras in the Elements and related writings have been recurrently suggested in the literature: a ‘stationary’ interpretation and an ‘instantaneous’ (specifically, temporary) one. Such persistent oscillations in the reading of Walras’s equilibrium concept lead one to suspect that some ambiguity or inconsistency may possibly exist within Walras’s original formulation of general equilibrium theory. In this paper we explore this conjecture focussing, in particular, on the relationship between the theory of the tâtonnement, regarded by Walras as an essential part of his overall equilibrium approach, and Walras’s own interpretation of the equilibrium concept as employed in the Elements. To this end we analyze the evolution of the tâtonnement construct over the four editions of the Elements published during Walras’s lifetime (1874-1877, 1889, 1896, 1900), separately referring to each of the four nested equilibrium models (exchange, production, capital formation, circulation and money) developed by Walras therein. From our analysis it turns out that either interpretation can indeed be traced back to Walras’s original treatment of the tâtonnement process and associated equilibrium notion in one or the other of the equilibrium models he puts forward in the various editions of the Elements: specifically, while the ‘instantaneous’ interpretation goes back to the exchange model, as dealt with in the second (1889) and subsequent editions, the ‘stationary’ interpretation is instead grounded in Walras’s theory of the tâtonnement process in production, as developed in the second (1889) and third (1896) editions of the Elements. Yet, it is only the ‘instantaneous’ interpretation to pass the internal consistency test, as Walras himself eventually realizes in preparing the fourth (1900) edition of his work, where in fact only the ‘instantaneous’ (specifically, temporary) equilibrium notion survives.