The correlation dimension and Lyapunov exponents have been calculated for two time series of atmospheric radon daughter concentrations obtained from four daily measurements during the period 1993--1996. A number of about 6000 activity concentration values of 222Rn and 220Rn daughters have been used. The measuring method is based on aerosol collection on filters. In order to determine the filter activity, a low background gross beta measuring device with Geiger-M¿ller counter tubes in anticoincidence was used. The small noninteger value of the correlation dimension (≃2.2) and the existence of a positive Lyapunov exponent prove that deterministic chaos is present in the time series of atmospheric 220Rn daughters. This shows that a simple diffusion equation with a parameterized turbulent diffusion coefficient is insufficient for describing the dynamics in the near-ground layer where turbulence is not fully developed and coherent structures dominate. The analysis of 222Rn series confirms that the dynamics of the boundary layer cannot be described by a system of ordinary differential equations with a low number of independent variables. ¿ 2001 American Geophysical Union