The acoustic theory of speech production relates articulatory maneuvers to acoustic attributes of speech. Some procedures are discussed that make use of this theory to analyze the vocalizations of nonhuman primates. These procedures make use of sound spectrograms, oscillograms, and computer-implemented analogs of the primate vocal apparatus as well as anatomical measurements. The use of these techniques in recent studies of nonhuman primate vocalizations is reviewed. These studies show that nonhuman primates lack the anatomical apparatus that is necessary for the production of the full range of human speech. Some unresolved questions concerning the structure of nonhuman primate utterances are discussed with regard to human linguistic ability.