Many economists have worried about changes in the demand for money, since money demand shocks can affect output variability and have implications for monetary policy. This paper studies the theoretical implications of changes in money demand for the nonneutrality of money in the limited participation (liquidity) model and the predetermined (sticky) price model. In the liquidity model, we find that an important connection exists between the nonneutrality of money and the relative money demands of households and firms. This model predicts that the real effect of a money shock rose by 100 percent between 1952 and 1980, and subsequently declined 65 percent. In contrast, we find that the nonneutrality of money in the sticky price model is invariant to changes in money demands or other monetary factors. Several researchers have concluded from VAR analyses that the effects of money shock over time are roughly stable. This view is consistent with the predictions of the sticky price model, but is harder to reconcile with the specific pattern of time variation predicted by the liquidity model.