Abstract : The measurement of the neutron electric dipole moment (nEDM) constrains the contribution of CP-violating terms within both the Standard Model and its extensions. The experiment uses ultracold neutrons (UCN) stored in vacuum at room temperature. This technique provided the last (and best) limit by the RAL/Sussex/ILL collaboration in 2006: dn < 2:9 × 10-26 e cm (90% C.L.). We aim to improve the experimental sensitivity by a factor of 5 within 2-3 years, using an upgrade of the same apparatus. We will take advantage of the increased ultracold neutron density at the Paul Scherrer Institute (PSI) and of a new concept including both, external magnetometers and a cohabiting magnetometer. In parallel, a next generation apparatus with two UCN storage chambers and an elaborate magnetic field control is being designed aiming to achieve another order of magnitude increase in sensitivity, allowing us to put a limit as tight as dn < 5 × 10-28 e cm (95% C.L.), if not establishing a finite value.