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We describe a simple way to construct new statistical models for spatial point pattern data. Taking two or more existing models (finite Gibbs spatial point processes) we multiply the probability densities together and renormalise to obtain a new probability density. We call the resulting model a hybrid. We discuss stochastic properties of hybrids, their statistical implications, statistical inference, computational strategies and software implementation in the R package spatstat. Hybrids are particularly useful for constructing models which exhibit interaction at different spatial scales. The methods are demonstrated on a real data set on human social interaction. Software and data are provided.