The emergent field of animal linguistics applies linguistics tools to animal data in order to investigate potential linguistic-like properties of their communication. One of these tools is the “Urgency Principle”, a pragmatic principle stating that in an alarm sequence, calls providing information about the nature or location of a threat must come before those that do not. This theoretical principle has helped understand the alarm system of putty-nosed monkeys, but whether it is relevant for animal communication systems more generally remains to be tested. Moreover, while animal communication systems can convey information via a large set of encoding mechanisms, the Urgency Principle was developed for only one encoding mechanism, call ordering. Here, we propose to extend this principle to other encoding mechanisms and empirically test this with the alarm call system of black-fronted titi monkeys (Callicebus nigrifrons). We investigated how information about the context of emission unfolded with the emission of successive calls. Specifically, we analysed how contextual parameters influenced the gradual sequential organization of the first 50 calls in the sequence, using methods borrowed from computational linguistics and random forest algorithms. We hypothesized that, if the extended Urgency Principle reflected the sequential organization of titi monkey alarm call sequences, mechanisms encoding urgent information about the predatory situation should appear before encoding mechanisms that do not. Results supported the hypothesis that mechanisms encoding for urgent information relating to a predator event consistently appeared before mechanisms encoding for less-urgent social information. Our study suggests that the extended Urgency Principle applies more generally to animal communication, demonstrating that conceptual tools from linguistics can successfully be used to study nonhuman communication systems.