We consider problems in modelling job-matching in the Czech Republic during the transition to a market economy. Special interest is devoted to functional form considerations and the analysis of returns to scale of the matching function. This explorative study aims to shed some light into the black-box of the matching technology by applying nonparametric estimation techniques which relax distributional assumptions. Nonparametric additive modelling enables us to evaluate the matching process locally for each combination of the underlying matching factors, rather than being restricted to global parameters. We apply these techniques to a rich panel of monthly observations of unemployment vacancies and unemployment-to-job exits in all 76 labor market districts in the Czech Republic between January 1992 and September 1996, and find non-linearities in the partial adjustment process as well as a partially negative coefficient of unemployment outows with respect to vacancies in some years. Moreover, we find locally increasing returns to scale in job-matching, which may be responsible for multiple equilibrium unemployment rates in the Czech Republic during the transformation process.