Basking sharks Cetorhinus maximus tend to aggregate in summer at favoured locations along Britain and Ireland's west coast. Sharks have been described approaching and close-following one another, often to one side. This has been interpreted as putative pre-mating behaviour. At aggregation sites around the Inner Hebrides we used boat-based observation and in-water and overhead drone video-photography to document behaviour and to determine the sex of individuals. It was confirmed that a shark will frequently move purposely towards another from a distance and swim to maintain a position either directly behind or closely to one side of a conspecific for short periods. Contrary to expectation, we found no relationship between the sex of a shark or its size and close-following. This suggests that following behaviours are not mainly related to courtship. Further, abrasions on the nose suspected to be related to male behaviour were found to occur on both sexes, although abrasions on pectoral fins, similarly suggestive of mating-related behaviour, were predominantly on females. Breaching by basking sharks has also been proposed as a means of attracting the opposite sex. We observed breaching by solitary sharks but commonly by sharks within aggregations, and at other times by more than one shark on the same day at the same time; but there was not any clear evidence to indicate that breaching is primarily related to mating. More likely individuals show close following chiefly for feeding-related hydrodynamic advantage. It remains plausible however that mature sharks make use of feeding aggregations to initiate pre-courtship behaviour.