Merseyside detectives investigating the murders of Bernadette Fox, 57, and her daughter Sarah Fox, 27, in Liverpool believe Peter Fox, who is wanted in connection with the attacks, may be in London or to have recently left the capital.
The bodies of Bernadette and Sarah were found at separate addresses in the Bootle area of the city last week.
Sarah Fox was discovered in Worcester Road at about 9.15pm on Thursday (16 April). She had been stabbed. Her mother Bernadette was found 200m away in Brookhill Road at around 4am on Friday. She died of asphyxiation.
Peter Fox, 26, who is Bernadette's son and Sarah's brother, is being urgently sought in connection with the double murder.
In a statement on Merseyside Police website Detective Chief Inspector Dave Rooney said: "The investigation into these deaths is at an early stage and although the motive is unclear at this time, we believe the offender may be known to the victims."
He continued: "We are currently trying to trace Peter Fox, the 26-year-old son of Bernadette, as he could have information which could assist with our investigation. I would appeal to Peter to come forward so that we can speak to him following the murders of his mother and sister."
Patrols in Bootle have been stepped up, said Rooney, but he went on: "We know that Peter travelled by train to London on Wednesday night and we are working with the Metropolitan Police to try and find him. Although we know he travelled to London that night he may well have gone on to travel outside of the London area.
"I would stress to the public that if they do see Peter Fox, they should not approach him. We would urge anyone with information about his whereabouts to contact the police on 999."
In a statement the Fox family said: "We are absolutely devastated following the loss of Bernadette and Sarah and are still trying to come to terms with what has happened to them both.
"Bernadette, who was a mother of three and grandmother of three, was a very outgoing and lovely person who wouldn't harm anyone. In fact she only ever had nice things to say about people. She was so caring and would help anyone.
"And Sarah was loved by her family and well-liked by her friends and neighbours. She was a fantastic aunty and was a cheeky, bubbly and outgoing person who loved her dog. They will both be greatly missed.
"We would ask that people appreciate that this is a sad and tragic time for the family and that we are left alone to grieve in peace, whilst we try to understand what has happened."
Peter Fox is described as white, between five foot two and five foot four inches tall, with short hair and slight build. Anyone with information regarding the murders or Peter's whereabouts can contact the Major Incident Room on 0151 777 3802/3938 or Crimestoppers on 0800 555 111.