The regional distribution of unemployment rates in the Czech Republic over the transition period is shown to be characterized by twin peaks, e.g. a high and a low unemployment equilibrium. The emergence of strong regional disparities at the beginning of the 1990s can, at least partially, be explained by regionally different degrees of competition between the emerging private sector and state-owned enterprises for skilled labor and the role of on-the-job transitions on the parameters of the matching function. This study presents a formalization of these effects and estimates empirical matching functions for a panel of labor market districts of the Czech Republic between January 1992 and July 1994. When time-series properties of unemployment to job exits are taken into account and dynamic panel estimators are applied, the Czech matching function is shown to exhibit increasing returns to scale, being consistent with multiple unemployment equilibria. Considering variables, which approximate the degree of job competition of employed workers in the search process, reveals strong heterogeneity of matching parameters with respect to the relative position of districts in the regional distribution of unemployment and vacancy rates, and the share of district employment in the private sector.