Police responded to a report of a fight in Montpelier Place at 10.15pm on Wednesday, 4 November.
A 40-year-old local man suffered stab injuries and was taken to Royal Sussex County Hospital for treatment, where he remains in a serious but stable condition.
Two 18-year-old men have been arrested on suspicion of attempted murder and remain in custody for questioning.
Detective Chief Inspector Gordon Denslow, of the Surrey and Sussex Police Major Crime Team, said: “We’d like to thank the public for their patience and understanding as our investigation into this matter progresses.
“This incident happened in a busy area of Brighton and we continue to appeal for anyone with any information – including any relevant CCTV, dash cam or mobile phone footage – to contact us.
“We are confident that someone knows what happened and would urge them to do the right thing and speak to us immediately. You can also contact Crimestoppers in confidence.
“The victim and suspects are believed to be known to each other and this is being treated as an isolated incident with no threat to the wider public.”
These are the fifth and sixth arrests made in connection with the investigation. Four other men, aged between 18 and 57, were arrested and have been released under investigation pending further enquiries.
You can report information either online or by calling 101, quoting Operation Moorcroft.