Sexually dimorphic characters of Onymacris plana, a dune-living, solitary tenebrionid beetle of the Namib Desert, were tested for their roles in male-male fighting over females. Males were smaller than females but had extraordinarily wide elytra, with great variance in this characteristic. In males, but not in females, elytra width increased with body length at an allometric scale. Male beetles were often aggressive towards each other, especially when mating or guarding females after mating or waiting for females at shady spots. Interactions were less intense when contesting over females on the open surface, where these fast-running beetles often overran each other in their attempts to retain their positions behind females until the females retreated into the sand, where mating took place. Winners of intrasexual fights and the successful mates of females tended to have longer bodies and wider elytra than the losers. Sexual selection appears to be the best explanation of the allometric scaling of the lateral extensions of male elytra. Sexual selection may furthermore contribute to other characteristics, such as large body length and long legs, that have ecological and ecophysiological significance.