Sleeping with the Enemy" would have been as well received as their first two albums together, though it's likely he would have made a bigger impact on the pop charts anyway.
Kilmer, who also starred in movies including Tombstone, was known for his work in the 1960s on the original "Batman" TV series.
He recently co-starred in the TV series "Curb Your Enthusiasm" and "The Legend of Bagger Vance."
In addition to his son Paul, Kilmer is survived by wife Barbara, children Rory, Sean and Kai, as well as seven grandchildren.
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