A 35-year-old man is being urgently sought by police following the separate murders of a 50-year-old woman and an 81-year-old man.
More than 100 officers are now involved in the search for James Allen following the deaths of Colin Dunford, in Middlesbrough, on Monday, and Julie Davison, in Whitby, North Yorkshire, yesterday.
Detectives have described the killings as "two brutal murders in the victims' own homes".
Cleveland Police and North Yorkshire Police issued a joint appeal to find Allen after officers linked the two murders.
Earlier today, detectives in Whitby described how Ms Davison was found dead by her sister at her flat on Church Square.
She had suffered serious head injuries.
Mr Dunford was found dead at his home on Leven Street, in Middlesbrough, on Monday.
A post mortem examination showed he also suffered serious head injuries as a result of a significant assault.
Temporary Detective Chief Superintendent Gordon Lang, head of crime operations for Cleveland Police, said: "We now believe the Middlesbrough murder is linked to the murder that took place in Whitby yesterday.
"Two brutal murders in the victims' own homes.
"Anyone who can carry out such callous acts needs to be caught as a matter of urgency.
"We have over 100 officers working on the incident to trace Allen and we are focusing our efforts in Cleveland and in
the Whitby area of North Yorkshire.
"Anyone who sees him or who knows where he is, we would ask them to contact 999 immediately."