In recent years, a number of studies have applied generalized additive models to time series data to estimate associations between exposure to air pollution and cardiorespiratory morbidity and mortality. If concurvity, the nonparametric analogue of multicollinearity, is present in the data, statistical software such as S-plus can seriously underestimate the variance of fitted model parameters, leading to significance tests with inflated type 1 error. This paper uses computer simulation and analyses of actual epidemiologic data to explore this underestimation of standard errors. We provide a method for assessing concurvity in data and an alternate class of models that is unaffected by concurvity. We argue that some degree of concurvity is likely to be present in all epidemiologic time series datasets and we explore through the use of meta-analysis the possible impact of concurvity on the existing body of work relating ambient levels of sulfate particles to mortality.