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Exposure to high levels of air pollution during the pregnancy is associated with increased probability of preterm birth (PTB), a major cause of infant morbidity and mortality. New statistical methodology is required to specifically determine when a particular pollutant impacts the PTB outcome, to determine the role of different pollutants, and to characterize the spatial variability in these results. We develop a new Bayesian spatial model for PTB which identifies susceptible windows throughout the pregnancy jointly for multiple pollutants (PM_2.5, ozone) while allowing these windows to vary continuously across space and time. We geo-code vital record birth data from Texas (2002–2004) and link them with standard pollution monitoring data and a newly introduced EPA product of calibrated air pollution model output. We apply the fully spatial model to a region of 13 counties in eastern Texas consisting of highly urban …