Abstract : The NEMO3 detector was designed for the study of double beta decay and in particular to search for the neutrinoless double beta decay process ($0\nu\beta\beta$). The intended sensitivity in terms of a half-life limit for the $0\nu\beta\beta$ decay is of the order of $10^(25)$~yr which corresponds to an effective neutrino mass $\langle m_\nu \rangle$ on the level of (0.3 -- 0.1)~eV. The $0\nu\beta\beta$ process is today the most promising test of the Majorana nature of the neutrino. The detector was constructed in the Modane Underground Laboratory (LSM) in France by an international collaboration including France, Russia, the Czech Republic, the USA, the UK, Finland, and Japan. The experiment has been taking data since May 2002. The quantity of $^(100)$Mo in the detector (7~kg) allows an efficient measurement of the two-neutrino double beta decay ($2\nu\beta\beta$) of $^(100)$Mo to the excited $0^+_1$ state (eeN$\gamma$ channel). Monte-Carlo simulations of the effect and of all the relative sources of background have been produced in order to define a set of appropriate selection criteria. Both Monte-Carlo simulations and special runs with sources of $^(208)$Tl and $^(214)$Bi showed that the only significant background in the eeN$\gamma$ channel comes from radon that penetrated inside the wire chamber of NEMO3. The experimental data acquired from May 2002 to May 2003 have been analysed in order to determine the signal from the $2\nu\beta\beta$ decay of $^(100)$Mo to the excited $0^+_1$ state and the corresponding background level. The physical result, which was obtained at the level of four standard deviations, is given in the form of an interval of half-life values at 95\% confidence level.