"The action was taken because of medical issues that have arisen for member David Crosby," the Web site http://crosbynash.com said in a posting on Friday which did not specify Crosby's illness.
An Australian newspaper reported earlier this month that Crosby had contracted pneumonia, which forced the postponement of a tour there.
Crosby and Nash were to have been joined in Australia by longtime partner Stephen Stills.
Crosby, 65, who has written of his years of substance abuse, has battled hepatitis C and had a liver transplant in 1995.
"We deeply regret that the band will not be able to embark on this (U.S.) tour as scheduled. At this time, we thank you for your understanding and the band looks forward to seeing you this fall," said manager Donald Miller in an announcement on the Crosby-Nash Web site.
The tour was to begin March 19 in Shawnee, Oklahoma and end April 15 in Niagara Falls, New York.
Crosby, Stills and Nash, playing also with Neil Young, comprised one of rock's biggest acts and embodied Woodstock-era folk-rock sensibilities of peace, love and music. They were known for hits including "Teach Your Children," "Woodstock" and "Marrakesh Express."
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