Police were called to the scene at Dalrymple Street in the centre of the Inverclyde town around 1.30am on Wednesday.
A 63-year-old man was found injured and taken by ambulance to Inverclyde Royal Hospital in Greenock, but died a short time later.
Police said a 44-year-old man has been arrested and charged in connection with the death.
He is expected to appear at Greenock Sheriff Court on Thursday.
Police said a 43-year-old woman has been arrested and charged with the alleged common assaults of two women aged 21 and a 22-year-old man.
She will be reported to the Procurator Fiscal separately.