Group-living animals travel together to collectively exploit the resources of their environment. This study investigates how social relationships and individual temperament traits affect movement orders in domestic cattle and sheep. We analysed spontaneous group movements occurring at pasture after a resting period in a group of 15 18-month-old Charolais heifers and a group of 19 1-year-old Romane ewe-lambs. For each species, animals had similar social experience and no kinship ties. Before that, animals were observed within the group to establish their social status (e.g. dominance and preferential relationships, and sociability), then in individual tests in order to assess their emotional traits. In both species, most individuals could initiate a group movement but some individuals were more successful than others in recruiting the rest of the group. Ewe-lambs, and to a lesser extent heifers, held preferential positions during travel. We did not find any significant correlations in either species between animal order and their position in the dominance hierarchy (heifers: P = 0.438; ewe-lambs: P = 0.574) while individuals linked by preferential bonds frequently followed each other during group movements (heifers: P < 0.001; ewe-lambs: P < 0.001). With regard to social traits, heifers with a low cohesion index, and with a lower number of partners with whom they develop frequent affinitive interactions, acted more frequently as ‘first movers’ (P = 0.040 and 0.023, respectively), as well as did ewe-lambs with a high spatial independency index (P = 0.002). Ewe-lambs with the highest cohesion indices were more frequently observed in front of the group while moving halfway between departure and arrival (P = 0.028). We did not find significant correlations between individual positions during group movements and emotional traits such as reactivity, boldness and fearfulness. We conclude that preferential bonds and individual traits related to social dependence were more influential in spontaneous group movements at pasture than were emotional traits and dominance status.