Private credit money forms are debt instruments that co-exist alongside publicly provided forms of money and emerge de-centrally out of the lending activities of banks or non-bank financial institutions. In normal times, they are easily convertible into higher-ranking forms of public or commodity money. Throughout history, however, private credit money forms have repeatedly become subject to a run by investors who all at once tried to convert their private credit money balances into higher-ranking money. Such runs are an integral and unavoidable feature of the modern credit money system, which in its essence is a self-referential network of expanding, yet instable debt claims. To keep up the stability of the monetary system, governments had to react to these runs and in a range of instances decided to drag the private credit money form under the control of the state by ensuring that they do not break away from par. This study examines this process of 'accommodating' private credit money. It establishes a functionalist theory about the transformation of the modern monetary system. To understand how and why such accommodation occurred, it develops an ideal-typical model of private credit money accommodation and applies it on three cases in the respective centres of the global financial system: the 1797 Bank Restriction in England that accommodated bank notes; the 1933 Emergency Banking Act in the U.S. that accommodated bank deposits; and the realignment of policies by the Fed and the U.S. Treasury in the 2008 crisis, which accommodated overnight repurchase agreements and money market fund shares as ‘shadow money’. On the basis of those case studies, the study argues that today’s public credit money supply is made up of accommodated, formerly private, credit money forms.