Police have named the murder victim as 31-year-old Stephen Davidson.
He was found dead in the living room of his house in the Ballyholme Road area of the town at around 5pm on Sunday.
Detectives believe Mr Davidson's killers may have been known to him.
A 40-year-old man and 30-year-old woman were arrested in the Bangor area shortly after 1pm on Monday in connection with the murder.
The woman is being held in Belfast and the man is in custody in Bangor.
It has not been established by police if Mr Davidson let the attackers into his house, or whether drugs were involved the murder.
Police are carrying out a number of searches in the Bangor area as part of their inquiries.
PSNI Detective Chief Inspector Richard Campbell said the investigation remained at an early stage.
It appears that he has been involved in some sort of altercation in the house and as a result of that he has sustained fatal injuries.
DCI Richard Campbell
DCI Campbell appealed for information about Mr Davidson's movements on Saturday night through to the time his body was discovered on Sunday.
"We know that he was in the Newtownards Road area of Bangor around 9.30pm on Saturday and I am very interested and very keen to speak to anyone who may have been with him at the time, or who may have been in contact with him or saw him between then and the time he was found here on Sunday evening," said the detective.
DCI Campbell said he also wanted to talk to anyone who was at Mr Davidson's address over this period.
The victim's next door neighbour Simon Cummings said he was shocked by what had happened.
"Total shock, disbelief, that it would happen one in Ballyholme, and two next door," he told UTV.
Mr Cummings and his young family have recently moved to the area, which he said was usually very quiet.
"The girls were terrified last night to see the police cars, but the police were very good, came in, spoke to the girls and reassured them that there was nothing to worry about," he added.
DUP MLA Alex Easton visited the scene. "We need to think about the family of this young man and pass on our condolences," he said.