The court heard that James Allen told a friend that he was dying of cancer on the night of one of the murders.
A friend of James Allen said that he took pity on him, and offered him somewhere to stay the night.
Allen is accused of murdering a pensioner in Middlesbrough last April, as well as a woman in Whitby.
The trial continues.
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Robert Hodgson, from Stanley, County Durham, committed the offences on the girls, aged as young as five or six, up to the age of 13.