The information in the pape is directed to those who develop and use damage functions which relate atmospheric degradation of materials to various causal agents in the atmosphere. Such relationships must be quantified mathematically as part of the overall cost-benefit considerations associated with possible pollution control strategies. Damage functions may be derived from theoretical considerations, from controlled experiments in environmental simulation chambers, from essentially uncontrolled field experiments, or from semicontrolled field experiments. The paper discusses optimum ways of combining these methods to improve the credibility and applicability of materials damage functions for use in assessments, with reference to some of the research performed for the National Acid Precipitation Assessment Program.