The NEMO-3 detector has been taking data in the Fréjus underground laboratory (LSM, France) since February 2003 and is devoted to the search for neutrinoless double-beta decay (0νββ). 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 for the half-lives are T1/2(0νββ) > 4.6 × 1023 yr for 100Mo and T1/2(0νββ) > 1.0 × 1023 yr for 82Se (90% C.L.). They lead to the following limits for the effective Majorana neutrino mass: 〈mν〉 < 0.7–2.8 eV for 100Mo and 〈mν〉 < 1.8–4.9 eV for 82Se. The half-lives of the two-neutrino double-beta decay (2νββ) have been measured for 100Mo, 82Se, 116Cd, 150Nd, and 96Zr and reported here as well.