A new class of analgesics is provided by substances that inhibit breakdown of endogenous substance such as enkephalins and/or endorphins. The analgesic effect of an enkephalin breakdown inhibitor is greatly enhanced by being combined with an antipyretic, anti-inflammatory analgesic, herein designated as an aspirin-type drug. Specifically, both D-phenylalanine and D-leucine, each an enkephalin breakdown inhibitor, when used separately provides excellent analgesia in animals and man without developing tolerance or addiction in either species. Use of a combination of D-phenylalanine and D-leucine provides a greatly enhanced analgesia approaching the analgesia achieved by morphine. Analgesia by the latter combination is very long-lasting in animals. The injection of a combination of D-phenylalanine and an aspirin-like drug that is antipyretic and anti-inflammatory, in an animal provides a greatly enhanced analgesia approaching the analgesia achieved by morphine. Analgesia by D-phenylalanine is very long-lasting in humans.