Research on reciprocity is impaired by confusing definitions and often wrongly used statistical tests. Here, two models of the mechanism on which reciprocity may be based are discussed and an initial step towards a new fremework for its analysis is presented. A distinction is made between reciprocity and interchange. In the case of reciprocity, for one kind of act the same kind is received in return. In interchange, however, two different kinds of acts are bartered. Three types of reciprocity/interchange in social actions among all pairs of group-members are distinguished (‘qualitative’, ‘relative’ and ‘absolute’) on the basis of the precision of the reciprocity/interchange. Permutation procedures for association between matrices (such as the Mantel Z and two other newly derived tests) are used as a statistical test for detecting reciprocity/interchange. A rough comparison of the power of the two new tests is included. The tests can be applied to all kinds of group-living animals and to all sorts of social behaviour. The distinction between the three types of reciprocity/interchange and the matching statistical methods are also useful for defining and detecting other patterns in social interactions, like unidirectionality and associations between different kinds of social behaviour. The influence on social interactions of variables like dominance rank, age and sex can be analysed in the three forms by testing correlations between invented matrices which represent the influence of these variables (the so-called hypothesis matrices) and social interaction matrices. These methods are extended for two categories of individuals, thus allowing the investigation of, for example, reciprocity between males and females. The methods are illustrated with examples of coalition formation and grooming behaviour among captive chimpanzees, Pan troglodytes.