Neonate ruminants produce distress calls when captured by a predator and discomfort milk begging calls when hungry. In many neonate ruminants, the distress and discomfort calls are high‐frequency vocalizations, in which the fundamental frequency is the key variable for recognition of their emotional arousal by caregivers. In contrast, in this study, we examine the low‐frequency open‐mouth distress and discomfort calls in the neonates of two species of wild‐living ungulates, which clearly highlight vocal tract resonances (formants). In the goitred gazelle (Gazella subgutturosa), the distress calls were higher in fundamental frequency (f0) and in the first and third formants than the discomfort calls. The accuracy of classifying individuals by variables of distress calls with discriminant function analysis (67%) was significantly lower than that of discomfort calls (85%). In the saiga (Saiga tatarica), only the third formant was higher in the distress calls than in the discomfort calls. The accuracy of classifying individuals by variables of distress calls (89%) did not differ significantly from that of discomfort calls (94%). Thus, the use of acoustic cues to vocal identity and to the degree of arousal differs between the two species. Calls were significantly more individualistic in the saiga, probably because this species lives in large herds and neonates use a ‘following’ antipredatory strategy, in which vocal individuality is crucial for mother–offspring communication. In contrast, goitred gazelles live in smaller groups and neonates use a ‘hiding’ antipredatory strategy. Accordingly, mothers can rely on additional environmental cues for spotting their young and this may decrease the necessity for individualization of the calls of neonates.