Among the various animals using acoustic signals for their communication needs, man and other primates are not the only ones who developed complex signals. We will show, with examples taken from the Brazilian fauna and recordings deposited into the Arquivo Sonoro Neotropical-ASN at the Campinas State University-UNICAMP, that different strategies exist for acoustic communication. Complex repertoires are found in species with complex social relationships. This is the case in some crickets (Endocous itatibensis, for example) and amphibians, like Hyla minuta, with sophisticated territorial and courting behaviour. In birds, the size and complexity of the repertoire is related to their social organisation and reaches a peak in gregarious jays (like Cyanocorax caeruleus) and anis (especially Guira guira). The "functional song'', that is the acoustic communication signals assuming the primordial function of species-specific recognition, expresses two opposite tendencies: the simplest unequivocal signal or the most varied one. The first solution is the most efficient if the signal is not degraded during its transmission, as are the double drumstrokes of the large Campephilus woodpeckers and the pure and unmodulated single whistle of some tinamous, doves, or owls like Glaucidium minutissimum. The other communication strategy consists in increasing the complexity of the signal, ensuring its reception through high redundancy and low monotony. It also permits the coding of populational and even individual identification cues, but must retain the specificity. Such a strategy is possible only by learning and some measure of interaction and creativity. Besides dialects, made of various parts, songs may show individual variations by different means: unique but stereotyped combination of sound elements as in Volatinia jacarina, multiplicity of fixed song types as in Cyclarhis gujanensis, versatility of the emission of different phrases (Cistothorus platensis) or notes (Turdus rufiventris, Augastes lumachellus). The song of the Humpback Whale Megaptera novaeangliae is a dialect combining a very long phrase with a largely predictable sequence. Versatility is increased by imitations as in the song of Turdus lawrencei. The challenge is to measure these diverse types of complexity.