The NEMO 3 detector, which has been operating in the Fréjus underground laboratory since February 2003, is devoted to the search for neutrinoless double-beta decay (beta beta 0v). The half-lives of the two neutrino double-beta decay (beta beta 2v) have been measured for 100Mo and 82Se. After 389 effective days of data collection from February 2003 until September 2004 (phase I), no evidence for neutrinoless double-beta decay was found from approximately 7 kg of 100Mo and approximately 1 kg of 82Se. The corresponding limits are T1/2(beta beta0v) > 4.6 x 10(23) yr for 100Mo and T1/2(beta beta 0v) > 1.0 x 10(23) yr for 82Se (90% C.L.). Depending on the nuclear matrix element calculation, the limits for the effective Majorana neutrino mass are <mv> < 0.7-2.8 e/v for 100Mo and <mv> < 1.7-4.9 eV for 82Se.