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 (ββ0ν). The half-lives of the two neutrino double-beta decay (ββ2ν) 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 ∼7 kg of ¹⁰⁰Mo and ∼1 kg of ⁸²Se. The corresponding limits are T_1/2(ββ0ν)>4.6×10²³ yr for ¹⁰⁰Mo and T_1/2(ββ0ν)>1.0×10²³ yr for ⁸²Se (90% C.L.). Depending on the nuclear matrix element calculation, the limits for the effective Majorana neutrino mass are 〈m_ν〉 < 0.7 — 2.8 eV for ¹⁰⁰Mo and 〈m_ν〉 < 1.7 — 4.9 eV for ⁸²Se.