Animal communication and human language have fundamental differences in their structures and functions. Furthermore, there is no living species demonstrating an intermediate stage of language evolution. Thus, we have difficulty in finding characteristics attributable to a communication system which can already be considered as a starting point for linguistic evolution. However, some findings coming from neurolinguistic research give us the opportunity to suppose that varying and arranging linguistic elements can be detached from other grammatical functions. Further information in this direction comes from apes' language-teaching experiments; namely bonobos (Pan paniscus) are able to understand and produce differences in meaning by varying word arrangements. Based on these results one can suppose that an acoustic signal system, which possesses discrete units for variable use, might be very ancient and might exist independent and prior to a more advanced language state. In the natural setting, acoustic territorial marking behaviour is exposed to selection pressure to elaborate sign systems built up from discrete, variable units. In addition to the well-known territorial bird songs, some monkey species and all species of lesser apes have territorial songs fitting these criteria. The analyses of the so-called long calls in chimpanzees and bonobos make it likely that the group-living great apes preserved the ability to create syntactically different calls, which would be developed by requirements of social life. A call repertoire emerged in these species, which contained a large number of call variants at group level available for each group member via social learning. This type of animal call is different from ordinary animal communication; it shows some features of human language. It can represent an intermediate stage between animal communication and language, and communication systems similar to this one can be considered as a starting point or first stage of language evolution.