A mathematical model of the biological protocol for the Mouse Lymphoma L5178Y Forward Mutation Bioassay is presented. The model relates the mutant progenitor frequency (MPF), the number of cells per million surviving cells with DNA damage after exposure to the chemical, to the mutant frequency (MF), the number of TFT-resistant cells per million survivors. For a given expression time, the deterministic relationship is linear and the proportionality constant depends on the relative suspension growth factor (rg) and relative cloning efficiencies (rc) of mutants to those of wild type cells: MF = (rg X rc) X MPF. Experimental noise leads to variations in the values of rg and rc and lack of reproducibility in the system. If mutant progenitors and their progeny grow as well as wild-type cells and if all of the parental mutant progenitors express the mutant phenotype, then rg = 1/2 and rc = 1. Biological mechanisms, such as differential growth characteristics of mutant and wild-type cells or DNA repair, can make the mutant frequency an inaccurate estimate of the MPF. For the assay to be useful as a screen for the mutagenic activity of chemicals, rg X rc has to be reasonably constant from chemical to chemical.