Police are treating the incident as attempted murder after two men were attacked and seriously injured during the incident.
Officer said at least four men were involved in a disturbance that spilled out onto the streets after a party last night.
The incident took place at around 11pm in Westmoreland Street in Govanhill.
Two of the men involved, aged 34 and 35, were seriously injured. They were taken to the city's Victoria Infirmary, where the 34-year-old is in a serious condition in intensive care. The other man was said to be stable. Extra police patrols have been brought in to the area.
Detective Inspector Alan McAlpine said: "The two injured men had been at a party nearby which appears to have spilled on to the street.
"We know that there were at least four men involved in the disturbance; the two in hospital and the suspects.
"From other witnesses there was a bit of a commotion outside which I am in no doubt that at that time of night people would have heard."
The first suspect is around 5ft 7in, bald, and at the time was bare-chested.
The second is 5ft 5in, and has dark brown hair. He was wearing a red t-shirt.
Anyone with information can contact officers on the non-emergency number 101, or Crimestoppers on 0800 555 111 where details can be given in confidence.