Subharmonics, deterministic chaos, biphonations, sidebands and frequency jumps, known under joining name nonlinear phenomena, represent acoustical appearances that occur in calls of various mammals, from insectivorous to humans. Although the physical basis for appearances of the nonlinear phenomen is known in principle, such aspects as occurrence and functional significance of nonlinear phenomena, are poorly understood. We described here the structural peculiarities of these appearances based on domestic dogs' whines demonstrating all kinds of the nonlinear phenomena. The nonlinear phenomena result directly from the work of mammalian vocal apparatus--lunges, vocal folds, and vocal tract, which are responsible for its inherent functional characteristics. The mammalian vocal folds represent a system of two coupled oscillators functioning in different vibratory regimes depending on degree of synchronization in their vibrations and occurrence of coupling between the vocal folds. This functioning does not need in direct neural control for turning on the complex regimes of vocal folds' vibration and switching from one regime to another. Besides, many mammals possess anatomical structures, such as vocal membranes, pads on vocal folds, or laryngeal air sacs, that are to participate in sound production as additional oscillators extend the range of possibilities for arising of nonlinear phenomena in vocalization. On the basis of published and own data, we provide and overview of the occurrence of nonlinear phenomena in sounds of humans, nonhuman primates, canids, and rodents, and discuss the supposed functional significance of these acoustical appearances in mammalian vocal communication systems. From one side, nonlinear phenomena may be related to various physiological disorders in humans and animals. In such cases, their appearance in calls may be nonadaptive, because they permit conspecifics' to avoid owners of such "ill" voices, and points easy prey to predators. From another side, in some cases the nonlinear phenomena may arise especially for performing of some signal functions in species communication system: to enhance reliability of individual recognition, to transmit information about size of a caller over the large distance, to permit individuals of not great size mimicry acoustically under more larger animal, to introduce variety into monotonous vocal sequences in order to force other group members to pay attention to a caller, and to facilitate distance estimation to a caller and direction of its movement.