We offer a model of perceptual intersubjectivity (PI), the phenomenon of two or more subjects focusing their attention on the same external target. The model involves two types: symmetric and asymmetric PI, and three levels: synchronous (SPI), coordinated (CPI) and reciprocal (RPI), defined on the basis of the observable behavior of the participants of (non-verbal) social interactions. We hypothesize that the three levels correspond to stages in the development and possibly evolution of human perceptual intersubjectivity, and provide support for this through an empirical study of adult-infant interactions in two species of great apes (chimpanzees and bonobos) and human beings. The results showed conspicuous and apparently qualitative differences between the human and non-human subjects, and clear developmental patterns in the human data. Thus our analysis may contribute to the ultimate goal of understanding the nature and development of human cognitive specificity, in line with goals with the collaborative project Stages in the Evolution and Development of Sign Use (SEDSU) [1] .