A significant outcome of this analysis concerns the existence of a monetary Walrasian equilibrium in the short run. We found indeed that whenever the traders' learning processes involve short-run rigidities of their expected real interest rates - which is the case in traditional neoclassical macroeconomic models - a short-run Walrasian equilibrium in which money has positive value may not exist. Real balance effects are then the essential regulating mechanisms of the economy, but they may be too weak to equilibrate the markets. As a corollary, in order to guarantee the existence of a short-run monetary equilibrium, one has to appeal to a stabilizing mechanism that was neglected by conventional neoclassical monetary theorists, namely, the intertemporal substitution effects that are induced by a variation of the traders' expected real interest rates. In the class of models that we have considered, this required basically that some or all traders' expectations about future prices and interest rates are to a large extent insensitive to the variations of current prices and rates of interest. The fact that such restrictions on anticipations are rather implausible shows that the existence of a short-run Walrasian monetary equilibrium raises more problems that neoclassical theorists like to believe.