A non-linear model for three competing social groups, each endeavouring to enlarge its size in a closed homogeneously mixing population is developed. Familiar examples of such a competition are provided by political parties, cults, sects etc. each trying to increase its area of influence in the society. The non-linearity of the model arises from the interactive processes involved in the process of conversion of members from one group to another. A special case dealing with the possibility of a mass-mediated external source for conversion is also considered. An interesting finding of the model is periodic variation in the size of each group with appropriately restricted values of the parameters of the model.