On March 14-17, 1982, the U.S. Environmental Protection Agency (EPA) sponsored the Mathematical and Empirical Receptor Models Workshop (Quail Roost II) at the Quail Roost Conference Center in Rougemont, NC. EPA invited 35 scientists to participate. Results of receptor modeling applied to real and simulated data sets were discussed, evaluated, and structured in a manner that permitted intercomparisons of the models. The participants also were asked to prepare reports on the state of the art of receptor modeling based on the results of their analyses of the simulated and real data. Topics covered in the reports are as follows: Overview of the Mathematical and Empirical Receptor Models Workshop; Review of Receptor Model Fundamentals; Interlaboratory Comparison of Source Apportionment Procedures: Results for Simulated Data Sets; Chemical and Physical Analyses of Houston Aerosol for Interlaboratory Comparison of Source Apportionment Procedures; Interlaboratory Comparison of Receptor Model Results for Houston Aerosol; and Considerations for Design of Source Apportionment Studies.