In some studies of atmospheric pollution, deposition data may be available from several distinct monitoring networks. Systematic differences may exist between networks, and an effective statistical analysis of the data combined from all networks should account for this possibility. This article develops a Bayesian modeling approach for spatiotemporal data from two monitoring networks that accounts for possible network differences in measurement error biases and variances. Wet sulfate deposition data from two networks in the eastern United States, the National Acid Deposition Program/National Trends Network and the Clean Air Status and Trends Network, are combined and analyzed via our modeling approach. We examine whether the temporal trend in deposition from 1989--1997 varies regionally and whether the measurement error biases and variances differ between networks. We also demonstrate how prediction uncertainty is reduced using the combined data from levels obtained when basing prediction on data from only one of the networks.