This contribution investigates two canonical sequence types (summons/answer and request/compliance sequences) in daily human-animal interactions. Primatologists inspired by sequential analysis have previously documented what can be referred to as “sequential patterns” in animal communication, which entail basic orientations to the normative expectations at the heart of social life. Moreover, recent studies have observed these forms of turn-taking in interspecies interactions. This investigation is a contribution to this emerging trend. Following a review of recent literature on the topic, both in the field of social cognition and in pragmatics, it analyzes natural interactions occurring between domestic animals (mostly dogs, but also horses and cats) and their caretakers in diverse contexts. It focuses on a set of typical adjacency pairs, examining the animals’ actions and uptakes as they appear in two sequential positions, ie. as first or second pair parts. I argue that unravelling the different ways in which animals’ actions may be “conditionally relevant” (Schegloff, 2007) to human utterances, and vice versa, has several critical consequences, both for the conception of animal participation and agency, as well as for the analytical devices that aim to develop linguistic and social theories.