Abstract : This work is part of the NEMO (Neutrino Ettore Majorana Observatory) experiment that is looking for an extremely rare radioactivity: the double beta decay without neutrino emission. Such process could prove the Majorana nature of the neutrino and could give an estimation of its absolute mass. The particularity of this experiment, currently running in the Modane underground laboratory (LSM), is the extreme weak signal (for T1/2 ~ 1024 years, a few events per year). It requires therefore very stringent conditions on all components of the background among which the level of radon and thoron activity. After a reminding of the general properties of radon and thoron as well as their influence on the NEMO data, this thesis focuses on the detection of these radioactive gases using the technique of electrostatic collection. The radon and/or the thoron daughters are collected by an electrostatic field on the surface of a silicon diode, where their characteristic alphas are detected. We have shown that the detection efficiencies are strongly influenced by the experimental conditions and that sensitivity around 1 mBq/m3 can be achieved for the radon in a gas. A series of measures through low background gamma spectrometer allowed us to understand the origin of the radon background, and thus showing that better sensitivity could be obtained by increasing the detection volume and by carrying out a strict selection of non-radioactive materials. For the thoron gas, which had never been studied before, the detection efficiencies have been found very low as a consequence of the short periods involved. Therefore, a continuous monitoring of the level of thoron in the NEMO gas is excluded, which underlines the importance for the NEMO experimental device to be able to control its own background.