At present, many experiments in particle physics are based on the requirement of the background as low as possible. Typically it is the case of experiments searching for neutrinoless double beta decay (0νββ). The IEAP CTU group has been involved for a long time in the NEMO 3 experiment which is studying neutrinoless and two-neutrino double beta (2νββ) decays of several isotopes. The NEMO 3 detector is located is the Fréjus underground laboratory in France. One of the main sources of background in this experiment is radon and its daughters. IEAP CTU is responsible in the NEMO Collaboration for the following tasks: measurements of radon activity, study of radon diffusion through different membranes used in the experiment, and study of radon emanation from construction materials of underground detectors. At first an apparatus for measurement of radon diffusion has been developed in IEAP CTU, in part in the framework of author’s Ph.D. study.