The GEM project is designed for the next generation 2β decay experiments with 76 Ge. One ton of "naked" HP Ge detectors (natural at the first GEM-I phase and enriched in 76 Ge to 86% at the second GEM-II stage) are operating in super-high purity liquid nitrogen contained in the Cu vacuum cryostat (sphere ⊘5 m). The latest is placed in the water shield ⊘11×11 m. Monte Carlo simulation evidently shows that sensitivity of the experiment (in terms of the T 1/2 limit for 0ν2β decay) is ≈10 27 yr with natural HP Ge crystals and ≈10 28 yr with enriched ones. These bounds corresponds to the restrictions on the neutrino mass m ν ≤ 0.05 eV and m ν ≤ 0.015 eV with natural and enriched detectors, respectively. Besides, the GEM-I set up could advance the current best limits on the existence of neutralinos -as dark matter candidates -by three order of magnitudes, and at the same time would be able to identify unambiguously the dark matter signal by detection of its seasonal modulation.