All members of the Bovini, including domestic cattle, have a more or less similar social behaviour, and so the aurochs probably showed the same behavioural patterns that all its relatives and descendants do. Only few aspects of the aurochs’ behaviour have been documented, mostly in Schneeberger’s report to Conrad Gesner from 1602. But most of what is described in this document is congruent with those of domestic cattle, for example the flehmen gesture, the way cows look for their calves or impressing behaviour by the bulls. All cattle have the same and comparably complex social and reproductive behaviour that also resembles the other bovine species, indicating that it is not greatly altered by domestication. Therefore I assume that the behaviour of the aurochs was very similar if not identical to that of domestic cattle. The following passages are based on observations of living domestic cattle (Camargue, Chillingham cattle, Heck cattle, Highland cattle, Galloway) and wild bovines as much as on Schneeberger’s report. I am going to use photos of more or less aurochs-like cattle on a relatively natural-looking background here to show the behaviour patterns described in the text.
Cattle form herds all year round, even tough Schneeberger reports that aurochs roam separately during summer . Probably he spotted single bulls since these usually separate themselves from the herds that are formed by cows and juveniles. These herds have a matriarchal structure  and wander around looking for feeding grounds. The usual herd size for cattle is between 20 and 30 animals . If the number of the animals within the herd grow larger, the herd splits up . The cows form sub groups of two or three animals that graze and rest together. The distance between the individuals depends on the social rank and lies between 0,5 and 3 meters . Friendly behaviour includes licking and stroking with the horns. Calves form “kindergarden groups” when their mothers are occupied with grazing and gestating, which are guarded by non-suckling cows or young bulls. The latter leave the herd at the age of 1,5 years when becoming sexually mature.
Adolescent bulls form bull groups, which is common to most bovines (therefore I was a little bit upset when an individual on deviantArt called this behaviour “speculative” commenting this illustration). These bull groups circle around the cow herds, and each group mates with cows of different herds each respective year, what can be interpreted as a mechanism against inbreeding . Bulls only join the herd during mating season. The common presence of bulls within cow/calf herds in some free-ranging domestic cattle populations might be explained by the loss of seasonality in the reproductive circle of domestic cattle . If the place is confined, cattle form a herd of all age classes and both sexes , so the herding behaviour apparently is plastic.
Older bulls from an age of 10 to 12 separate from the bull group to avoid the constant competition with the other bulls. These old bulls are solitary, territorial and do not partake in reproduction anymore. The maximum life expectancy of cattle is about 20 years . In wild aurochs it probably was a little shorter, and also Schneeberger reported that aurochs lived for only 15 years .
When cattle are alarmed or start to flee, they do not stray up but stay close together. Like many other large ungulates, they form a defensive circle around their calves .
Cattle are hierarchic animals and there is a dynamic social order within a herd. This order is not linear but polygonal, f.e. C < A < B < C. The higher the rank of an animal the higher the quality of food and resting places, and the lower the level of stress because a lower rank in the hierarchy means that is constantly dominated by other herd members. Dominating behaviour includes display like standing in front of the opponent in an angle of 90° and elevating the head to show off its full size, or hits with the horns and pushing the individual aside. If the conflict does not end here, a combat fight follows, which is carried out head-to-head by pushing and pulling the opponent with the horns until it retreats. The winner might chase the loser for a few seconds. Harsh fights take place by bulls as much as cows [2,3,4,5]. Free ranging cattle, especially bulls, often show the results of such fights: scars along the neck and shoulders, broken-off horn tips, ear cuffs ripped apart, and sometimes even a stabbed eye. Superiority does not necessarily depend on mass and strength only – the size and shape of the horns plays a role as well, as much as the psyche of the animal [3,4].
Bulls also show off their strength by throwing dust and plant material into the air with their horns and hooves (which is also reported by Schneeberger), omitting a growling sound. Bulls in a rut also make repetitive, trumpeting sounds which I guess are used to attract cows and intimidate other bulls. For videos showing the behaviours I just described, see here, here, here and here.
Cattle form harems during the mating season, which under natural circumstances usually takes place during late august* . The traditional image that one bull conquers a harem and is the only male who covers the cows is not correct. In fact there is a number of other bulls that seize their chances when the leader of the harem is busy at the moment, but it is the cow’s choice which bull mates with her. Bulls in heat show the so-called flehmen gesture by curling back their upper lip and stretching out the tip of the tongue in order to detect pheromones and other scents with their vomeronasal organ. After three days of testing the cow’s scent and urine, the bull mates with the cow. Friendly behaviour between bull and cow like licking and stroking with the horns usually are restricted to the mating season.
* Domestic cattle in man’s custody mate all year round, but if exposed to natural factors and natural selection in particular, their reproductive circle becomes seasonal again like in all large wild mammals. Aurochs apparently had the same rhythm.
After mating, a nine month-long pregnancy starts. The behaviour of the cow immediately before birth probably depends on habitat . If forest edges and bushes are available as shelter, the cow separates from the herd a few days or hours before birth [3,5]. On open grassland, the cows might tend to calf near to the herd . The new-born calf immediately tries to make its first step while the mother is licking its wet fur . The placenta arrives a few hours after birth and is consumed by the mother. As soon as the calf is able to walk, the cow takes it away from the birth site to not attract predators. The first milk the calf consumes is called colostrum and is very alimentary. The mother-calf bond is formed within three days. Mother and calf recognize each other by scent, voice and looks. While the mother grazes in the herd, the calf is hidden between bushes or at a forest edge, where it is exposed to predators [1,5].
 van Vuure, Cis: Retracing the Aurochs - History, Morphology and Ecology of an extinct wild Ox. 2005
 Meissner & Limpens: Dedomestikation – wilde Herden zwischen den Menschen. 2001
 Julia Poettinger, 2011: Vergleichende Studie zur Haltung und zum Verhalten des Wisents und des Heckrinds.
 Annette Perrey: Die Sozialstruktur einer Herde Auerochsen im Wildgehege Neandertal. 1999
 Frisch, Walter: Der Auerochs – das europäische Rind. 2010.