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This paper deals with the clustering of data generated by spatio-temporal point processes. The interest on this topic is motivated by the recent availability of spatio-temporally indexed data in several applicative fields like seismology, climatology, economics, social sciences. The data we analyse is a collection of instantaneous events, each occurring at a given spatial location.  We introduce a strategy which finds a partition of the individuals into homogeneous clusters considering the space-time interactions. We transform the spatio-temporal point process into two marked point processes, considering the times as marks of the spatial point process and the locations as marks of the times. This allows to use the marked variograms to describe the second-order characteristics of the individuals, in time and space. We propose a k-means like algorithm which uses the marked variograms as cluster representative and performs the allocation to clusters evaluating the contribution of each individual to the definition of the marked variograms. This allows to get clusters of individuals which are homogeneous in terms of space-time interactions.