After analysis of 5797 h of data from the detector NEMO 3, new limits on neutrinoless double beta decay of ¹⁰⁰Mo (T_1/2 > 3.1 × 10²³ y, 90% CL) and ⁸²Se (T_1/2 > 1.4 × 10²³ y, 90% CL) have been obtained. The corresponding limits on the effective majorana neutrino mass are: 〈m_ν〉< (0.8 – 1.2) eV and 〈m_ν〉 < (1.5 – 3.1) eV, respectively. Also the limits on double-beta decay with Majoron emission are: T_1/2 > 1.4 × 10²² y (90% CL) for ¹⁰⁰Mo and T_1/2 > 1.2 × 10²² y (90% CL) for ⁸²Se. Corresponding bounds on the Majoron-neutrino coupling constant are 〈g_ee〉 < (0.5 – 0.9) × 10⁻⁴ and < (0.7 – 1.6) × 10⁻⁴. Two-neutrino 2β-decay half-lives have been measured with a high accuracy, T_1/2^100Mo = [7.68 ± 0.02(stat) ± 0.54(syst)] × 10¹⁸ y and T_1/2^82Se = [10.3 ± 0.3(stat) ± 0.7(syst)] × 10¹⁹ y.