Opposing approaches to money competition that state that all monetary forms are substitutes, theories of complementarity state that some can be complementary. This text analyses the ways in which monies can be linked by drawing upon the variety of so-called contemporary community and complementary currencies (CCCs). It considers four basic binary relations between monetary assets: commensurability, convertibility, co-use and coincidence of spheres of uses. Through their combinations, four means of linking monies are identified: substitutability, simultaneity, supplementarity and autonomy. On this basis, unpacked competition and complementarity do not oppose each other but appear to be related. The less forms of money are built on specific social values, the more complementarity may be pervaded by competition. This paper illustrates how this framework can be used with cases of the Argentine trueque (‘barter’) and the French experimental SOL. Both experienced difficulties that show the complexity of the links, possible shifts and their effects on the sustainability of the schemes.