Turn beginnings are the place in conversation where the connection (or otherwise) between a prior and a next turn is displayed. This crucial interactional task is usually fulfilled by turn-initial particles, specifically those known as discourse markers. Although the use of discourse markers by second or foreign language speakers has actually been largely discussed in the previous literature on interlanguage pragmatics, studies that focus on turn-initial discourse markers and that are conducted from a conversation analytical perspective are still scarce. The aim of this paper is therefore twofold. On the one hand, it makes a case for the use of conversation analysis as a research methodology for the study of discourse markers in a second or foreign language. On the other hand, and as a practical elaboration, this paper investigates the use of the discourse markers “y” and “sí” in the turn-initial position by foreign language speakers of Spanish. The results show that both discourse markers are part of an overall concern of signalling continuity and affiliation even in topic shifts and in non-aligned turns.