NONFICTION : KOOP: The Memoirs of America’s Family Doctor <i> by C. Everett Koop, M.D. (Random House: $22.50; 332 pp.)</i>

While we may remember Koop as the man who stood proudly in his stark white admiral’s uniform ready to lead his fleet of hospitals into battle against the nation’s health problems, his authority in the Reagan Administration is perhaps better symbolized by his first day at work. Told to report to a little office, starkly empty except for a desk and chair, he busies himself cleaning the dusty room until, “hours later,” he is finally introduced to his new boss. Things spiral down from there. Ridiculed first by liberals as “Dr. Kook” or “Dr. Unqualified” and then by conservatives, he is advised by a Hill sage to “keep your head down and your mouth shut.”

Koop ignores the advice, emboldened, like Mr. Smith gone to Washington, by the view outside his little window--an American flag flapping briskly in front of the Capitol dome--and by the memory of his earlier success as a pediatric surgeon in reducing the mortality rate of newborns. Like many surgeons, Koop is more a man of action than reflection, and so his reasoning is sometimes glib: When presented with Siamese twins sharing the same heart, for instance, he resolves the problem by observing that “The smaller was essentially a parasite on the other. It was clear we had no choice about which twin would have to be sacrificed.” But Koop’s stinging indictment of our health-care system is shocking coming from someone who served for so long at its helm. Calling it “our dysfunctional health care system,” “our health scare system” and “our health care non -system,” Koop advocates a “thorough overhaul” of an industry that spends more and more money to serve fewer and fewer people.