A nonparametric Bayesian model is proposed for segmenting time- evolving multivariate spatial point process data. An inhomogeneous Poisson pro- cess is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two di®erent inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an ap- proximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincin- nati, Ohio, USA. © 2012 International Society for Bayesian Analysis.