The attack happened area at around 9.30 pm in the Donegall Road last night.
Detective Sergeant Kenneth Leckey said: “One of the males sustained a serious head injury and is currently described as being in a critical condition in hospital.
“The second male sustained facial injuries which are not believed to be life threatening.
“The assault occurred whilst a band parade was taking place in the area.”
However, the attack is not believed to be sectarian.
Sergeant Leckey added, “It is understood that the two males are brothers and I would appeal to anyone who was in this area and witnessed the assault to contact police on the non-emergency number 101.
“Or alternatively contact Crimestoppers anonymously on 0800 555 111.”