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 as well as rural areas. Our results indicate significant signal in the first two trimesters of pregnancy with different pollutants leading to different critical windows. Introducing the spatial aspect uncovers critical windows previously unidentified when space is ignored. A proper inference procedure is introduced to correctly analyze these windows.