So bad was the problem, the book says, that at the height of the Vietnam War the then Secretary of Defence, James Schlesinger, ordered military commanders not to react to orders from the White House, unless they were cleared with him or the secretary of state.
The claims appear in The Arrogance of Power: The Secret World of Richard Nixon by Anthony Summers, who also alleges that Mr Nixon beat his wife, Patricia, on more than one occasion, once giving her a black eye.
Mr Nixon resigned from office in 1974 over his role in the Watergate scandal, becoming the only sitting US president in history to step down to avoid impeachment.
He died on 22 April, 1994.
Depression
According to the book, Mr Nixon consulted a psychotherapist, Dr Jack Dreyfus, in 1970 after becoming depressed over the hostile public reaction to the bombing of Cambodia.
The psychotherapist said Dilantin, an anti-convulsant used to counter epilectic seizures, was effective in combating "fear, worry, guilt, panic, anger and related emotions, irritability, rage, depression, violent behaviour" and a host of other ailments.
The New York Times quoted a specialist from Cornell University Medical School as saying that Dilantin had potentially serious side effects, such as changed mental status, confusion and loss of memory.
'Marital abuse'
Mr Nixon's family and friends strongly deny that he took mood-altering drugs.
They also deny the claim that the relationship between Mr Nixon and his wife, Patricia, was one of "prolonged marital difficulty, of physical abuse".
Mr Nixon elder daughter, Tricia Nixon Cox, told the Associated Press that she could "state unconditionally that at no time during 1962 or ever did my father ever strike my mother or did my mother ever have physical signs or bruises of the type claimed in this book".
She said her mother would have walked out immediately if she had been subjected to that kind of treatment.
She also said that although she did not know what medication her father was taking, if any, his personality and mood did not change while he was president.
She said he was always averse to taking any kind of drugs, even declining painkillers at the dentist.