The incident was reported to have taken place between 5am and 5.40am on Saturday 14 December 2024 on the London-bound carriageway, between the A2050 and the A28 near the exit for Wincheap, Canterbury.
A silver Mercedes-Benz C Class and white Seat were involved and the victims were assaulted on the side of the carriageway.
One man was taken to a London hospital with serious injuries and a second man is being treated at a local hospital.
Officers are appealing for anyone who saw this incident, or either of the vehicles in the moments leading up to it, to come forward and speak with them.
Drivers are also urged to check dashcam for any important footage.
Anyone with information should call 01303 289600, quoting reference 14-0241.
CCTV or dashcam footage and information can also be submitted via the public portal here.
You can also contact Crimestoppers anonymously on 0800 555111, or by using the online form on their website.