We present a monetary model with segmented asset markets that implies a persistent fall in interest rates after a once-and-for-all increase in liquidity. The gradual propagation mechanism produced by our model is novel in the literature. We provide an analytical characterization of this mechanism, showing that the magnitude of the liquidity effect on impact, and its persistence, depend on the ratio of two parameters: the long-run interest rate elasticity of money demand and the intertemporal substitution elasticity. The model simultaneously explains the short-run "instability" of money demand estimates as well as the stability of long-run interest-elastic money demand. (JEL E13, E31, E41, E43, E52, E62) T his paper unifies two main views, or theories, on money demand. One is the transactions-based money demand that emerges in the models of, e.g., BaumolTobin or Sidrauski. This theory predicts a stable downward sloping relationship between real balances and interest rates. This relationship is apparent in the lowfrequency data, e.g., those describing decade to decade movements. The second theory is the so called "liquidity effect," namely that a central bank's purchase of bonds, which increases the amount of money, creates a transitory but persistent decrease in interest rates. These patterns are apparent in high-frequency data, such as those used in the VAR literature for the identification of monetary shocks. This paper presents an analytically tractable model with segmented asset markets that unifies both ideas, displaying a stable long-run money demand, and explaining its short-term "instability" in terms of the liquidity effect. A new element of our model is a full characterization of the gradual propagation mechanism of monetary shocks in terms of a few structural parameters.