The emergency services were called to a home on Thorold Road in Chatham at around 3.15am yesterday (December 2).
Paramedics treated a 19-year-old man for stab wounds but the victim died at the scene.
A 32-year-old man from Chatham, was arrested later the same day.
That evening, an 18-year-old from Greenford in Ealing was also arrested. Both remain in custody.
A cordon remains in place at the scene of the stabbing in Thorold Road as enquiries continue, though an adjacent alleyway has been reopened.
Detectives continue to appeal for witnesses and anyone with CCTV or dashcam footage to come forward.
Anyone with information is asked to call 01622 652006, quoting reference 46/206765/25, or submit it via the dedicated online portal.
You can also report anonymously via Crimestoppers by calling 0800 555111 or completing the online form.
