The need for a stable monetary policy arises from several facts about business cycles. For example, practically all recessions in industrial countries were preceded by restrictive measures of central, banks. The main cause for the instability, however, was the expansionary policy that led to a boom and too high inflation. There is no question that high inflation in the long run is caused by high money growth; the empirical evidence in favor of the quantity theory of money is overwhelming. Inflation reduces economic growth considerably if it exceeds a certain level. At rates below 10 percent, the negative effects appear to be small. But recent studies show that there is a tremendous welfare gain even if inflation is reduced from a low rate of two percent to zero. This follows from the existence of distorting taxes and from a high demand for non-interest bearing cash at low rates of interest. The conclusion is that zero inflation can be achieved and that it produces a sizable free lunch for a society. While there is a consensus that monetary policy should follow a rule because discretionary policies have a bias towards higher inflation, it is not clear what the best strategy should be. It is often stated that monetary targeting cannot be used in the case of an unstable money demand function. This is not necessarily true because this instability can often be taken account of. Actually, rules exist according to which money growth adjusts to changes in the trend rate of the velocity of money. An instability of the money demand function does not invalidate the policy of monetary targeting or the main predictions of the quantity theory of money. The instability of money demand has led many central banks to pursue inflation targeting instead. But this policy, too, is fundamentally affected if the demand for money is not stable: The strategy requires a forecast for inflation which critically hinges on the conditions on the money market. In the case of an instability, it is difficult or even impossible to predict inflation accurately. This means that inflation targeting may not be better than monetary targeting. According to the Taylor rule, which is often propagated, the central bank reacts to the output gap as well as to the difference between actual inflation and the inflation target. If the central bank wants to set the short-term interest rate accordingly, an estimate for the real equilibrium interest rate is needed. Given the large variations in the trend of real short-term interest rates in the past, it is quite possible that a central bank uses a "wrong" estimate when following the rule. A small underestimation may already produce considerably higher inflation. Such an error is equivalent to the error concerning the estimate of trend velocity in the strategy of monetary targeting, so both strategies may lead to deviations from the target inflation rate. In other words: The Taylor rule is not necessarily superior. The future European Central Bank will choose between monetary targeting and inflation targeting. The start of the European Monetary Union may lead to an instability of the demand for money because of the regime shift. Therefore, the strategy of monetary targeting may lose some of its appeal. However, it does not follow that it is better to pursue a policy of inflation targeting. Any strategy will have difficulties when the fundamental link between money, prices, income and interest rates is disturbed. The rules for monetary policy have desirable features: inflation is to be kept under control, and fluctuations of output are to be reduced. But obviously, there is no single rule which is always and everywhere better than the alternatives. To conclude: It is not justified to disregard monetary targeting — a tendency which seems to prevail among central bankers and economists alike. After all, the quantity theory of money holds well enough to stress the importance of monetary aggregates as an anchor for the price level.