Modular multilevel converters (MMCs) are the basic building blocks of multi-terminal direct current systems (MTDCs). The current rapid growth of such systems makes it imperative to develop methods to analyse their DC-side stability, thereby ensuring a correct overall operation. In this paper, starting from a simplified MMC model, general conditions for DC-side stability are derived. These conditions have been validated by simulating a point-to-point high voltage direct current system and an MTDC network. MMC models of different degrees of accuracy have been adopted to show that the conditions derived in the paper hold with a good degree of approximation even when more detailed representations are considered.