The claims against Travis -- a 69-year-old former top BBC broadcaster nicknamed "The Hairy Cornflake" -- emerged after a number of women contacted police investigating abuse by another BBC star, Jimmy Savile.
His alleged victims said he acted "as if he had a perfect right to touch their breasts or put his hands in their clothing to grope them," prosecutor Miranda Moore told London's Southwark Crown Court.
The offences allegedly happened when Travis was working as a DJ or entertainer, such as starring in a pantomime, or in his home when he was being interviewed, Moore added.
The charges, which he denies, span the period between 1990 and 2008.
Travis, who is charged under his real name of David Griffin, was one of the biggest names in British broadcasting in the 1970s and 1980s.
His fans included Myanmar opposition leader Aung San Suu Kyi, who listened to his shows while under house arrest.
He hosted the breakfast show on BBC Radio 1, Britain's main pop music station, between 1978 and 1980.
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