Officers were called to a report of a large group of people fighting on Marine Parade, Brighton, at 5.20am on Sunday (December 1).
As they responded, it was reported that three of the group had then been struck by a vehicle.
Police said the victims were taken to hospital with serious injuries. A 20-year-old man is in a critical condition and an 18-year-old man and 22-year-old man are in a serious condition.
A 32-year-old man was arrested on Sunday on suspicion of causing grievous bodily harm and a 33-year-old man was detained on suspicion of attempted murder on Monday morning (December 2). They are both in custody.
The vehicle, a BMW X6, was later found abandoned nearby.
Detective Chief Inspector Chris Friday: “This is a fast moving investigation and we are again appealing for anyone who may have seen the incident or has any information about it to come forward.
“We are particularly keen to hear from anyone who may have mobile phone footage, dashcam footage or anyone with private CCTV footage of the incident.
“Marine Parade is likely to remain closed between the pier roundabout and Camelford Street until Tuesday afternoon (3 December) while we are continuing searches and carrying out enquiries and I would like to thank the public for their patience.”
The incident is not terror-related, police said.
If you can help with the investigation please report online or ring 101 quoting Operation Danebridge.