Recent research has shown that money substitutes - whether in the form of foreign currency or of more exotic instruments such as privately-issued moneys - are common in developing and transition countries, and have important consequences for macroeconomic and financial sector policy. The aim of this thesis is to advance our theoretical and empirical understanding of the determinants of money substitution in developing and transition economies. We begin in Chapter 1 by addressing the need for a general theoretical framework for the analysis of money substitutes. Reviewing both the classical and the modern theoretical literature on money, we conclude that the Credit theory of money - an ancient but until recently neglected theory which conceives of money as a unilateral financial contract between its issuer and its bearer - is a useful framework for such analysis. In Chapter 2, we undertake an empirical analysis of non-cash settlements (NCS) in Croatia. Using time series econometric analysis, we demonstrate that the instruments used to settle NCS are at least in part substitutes for the national currency, created endogenously by the enterprise sector in response to constraints on their participation in the official monetary and banking system. We turn to the most important form of money substitute in developing and transition countries - foreign currency - in Chapter 3, where we present a new review of the theoretical and empirical literature on dollarisation. In particular, we track the evolution of theoretical models of dollarisation in response to the increasing empirical importance of financial dollarisation relative to currency substitution. In Chapter 4 we undertake an empirical study of the determinants of deposit dollarisation in the two transition economies of Estonia and Lithuania by building and interpreting dynamic, multiple equation, econometric models. We find that a simple, portfolio theoretic account of the dollarisation process furnishes a good explanation, but also that data availability limits the level of analytical detail that this approach can attain.