The brothers -- Ahmed Vawda, 25, an accountant and Mohamed Vawda, 31, an estate agent -- and the man were tenants in the same building in Durban.
Residents claimed that Ahmed was walking with his wife towards the elevators after parking his car when he was shot twice by the man on Sunday.
Mohamed heard an argument from his third-floor flat and went downstairs. When he stepped into the parking lot, he was also shot dead.
Refusing to be named, he said there were frequent arguments between the brothers and the alleged shooter over preferential parking spots in the limited parking bays in the building.
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"The situation is especially bad at weekends, when visitors come to the building and sometimes take over bays allocated to other tenants," the resident said.
Neighbours of the deceased said the man is believed to have just returned from a firearm training session at a nearby shooting range when the incident occurred, as he had been carrying target boards with bullet holes in them.
Police have arrested the killer, who was not identified.