Mould growth was modelled on fermented bakery product analogues (FBPA) of two different pH (4.5 and 5.5), different water activity (aw) levels (0.80–0.90) and potassium sorbate concentrations (0–0.3%) by using seven moulds commonly causing spoilage of bakery products (Eurotium spp., Aspergillus spp. and Penicillium corylophilum). For the description of fungal growth (growth rates) as a function of aw, potassium sorbate concentration and pH, 10-terms polynomial models were developed. Modelling enables prediction of spoilage during storage as a function of the factors affecting fungal growth. At pH 4.5 the concentration of potassium sorbate could be reduced to some extent only at low levels of aw, whereas at pH 5.5 fungal growth was observed even by adding 0.3% of potassium sorbate. However, this preservative could be a valuable alternative as antifungal in such bakery product, of slightly acidic pH, if a long shelf life has not to be achieved.