The 83-year-old Harris said little during an appearance in Westminster Magistrates Court, the Daily Mirror reported.
Harris seemed somewhat confused. When he was asked for his name, address and birth date, he identified himself and then asked "What was the next thing?"
He was released on bail pending an appearance in Crown Court in October.
Harris allegedly assaulted two teenage girls, one in 1980 and 1981, the other in 1986. He is also charged with taking indecent pictures of children in 2012.
A native of Australia, Harris came to England in 1952 to study art and began his television career the next year by drawing cartoons on a children's program.
His song, "Tie Me Kangaroo Down, Sport," was a hit in Britain, Australia and the United States.
In 2005, Harris painted Queen Elizabeth to mark her 80th birthday. He was honored the next year as a Commander of the British Empire and also performed at a Diamond Jubilee concert.
Harris was arrested in March as part of Operation Yewtree, the investigation into sex crimes in the entertainment industry that began with allegations involving the late Jimmy Savile. He was charged in August.