Fine particulate matter (PM(2.5)) is an atmospheric pollutant that has been linked to serious health problems, including mortality. PM(2.5) is a mixture of pollutants, and it has five main components: sulfate, nitrate, total carbonaceous mass, ammonium, and crustal material. These components have complex spatial-temporal dependency and cross dependency structures. It is important to gain insight and better understanding about the spatial-temporal distribution of each component of the total PM(2.5) mass, and also to estimate how the composition of PM(2.5) might change with space and time, by spatially interpolating speciated PM(2.5). This type of analysis is needed to conduct spatial-temporal epidemiological studies of the association of these pollutants and adverse health effect.We introduce a multivariate spatial-temporal model for speciated PM(2.5). We propose a Bayesian hierarchical framework with spatiotemporally varying coefficients. In addition, a linear model of coregionalization is developed to account for spatial and temporal dependency structures for each component as well as the associations among the components. We also introduce a statistical framework to combine different sources of data, which accounts for bias and measurement error. We apply our framework to speciated PM(2.5) data in the United States for the year 2004. Our study shows that sulfate concentrations are the highest during the summer while nitrate concentrations are the highest during the winter. The results also show total carbonaceous mass.