Numerous studies have shown a positive association between daily mortality and particulate air pollution, even at concentrations below regulatory limits. These findings have motivated interest in the shape of the concentration-response relation. We developed flexible modeling strategies for time-series data that include spline and threshold concentration-response models. We applied these models to daily time-series data for the 20 largest US cities for 1987 through 1994, using concentration of particulate matter less than 10 microm in aerodynamic diameter (PM10*) as the exposure measure. The spline model showed a linear relation without indicating a threshold for the relative risks of death for all causes (total deaths) and for cardiovascular-respiratory causes in relation to PM10 concentration. By contrast, for causes other than cardiovascular-respiratory, the relative risk did not increase until the concentration reached approximately 50 microg/m3 PM10. For total mortality, a linear model without threshold was preferred to the threshold model and to the spline model, using the value of the Akaike information criterion (AIC). The findings were similar for combined cardiovascular and respiratory deaths. These findings indicate that linear models without a threshold are appropriate for assessing the effect of particulate air pollution on daily mortality even at current ambient levels.