Interlayer magnetoresistance of the Bechgaard salt (TMTSF)2NO3 is investigated up to 50 teslas under pressures of a few kilobars. This compound, the Fermi surface of which is quasi twodimensional at low temperature, is a semi metal under pressure. Nevertheless, a field-induced spin density wave is evidenced at 8.5 kbar above ∼ 20 T. This state is characterized by a drastically different spectrum of the quantum oscillations compared to the low pressure spin density wave state. PACS numbers: 75.30.Fv, 72.15.Gd, 71.18.+y Bechgaard salts (TMTSF) 2 X, where TMTSF stands for tetramethyltetraselenafulvalene and X is an inorganic anion, have been widely studied over the past twenty years for their very complex (pressure, magnetic field, temperature) phase diagrams that involve quasi-one dimensional (q-1D) metallic, spin density wave (SDW), superconducting and field-induced spin density wave (FISDW) states (for a review, see Refs.[1]). Nevertheless, FISDW phenomenon is still attracting experimental [2] and theoretical [3] studies. In the framework of the quantized nesting model [4] and its latest refinements [3], orbital effects stabilize SDW states in compounds with q-1D Fermi surface (FS) at low temperature through the increase of the 1D character of the electronic movement. Furthermore, it has also been stated that a FISDW can only occur provided the groundstate is superconducting [5]. In line with both of these predictions, a FISDW has so far only been observed in Bechgaard salts with both a superconducting groundstate and a q-1D FS, e. g. in slowly cooled (TMTSF) 2 ClO 4 at ambient pressure or (TMTSF) 2 PF 6 under pressures of a few kilobars. In contrast, a FISDW has also been reported in (DMET-TSF) 2 AuCl 2 which remains a q-1D metal at least down to 42 mK [6]. It should also be mentioned that a field-induced insulating phase, essentially driven by Pauli effects, has been evidenced in τ -phase organic metals with q-2D FS [7]. The aim of this paper is to argue that, at variance with the above theoretical statements, a FISDW state can be observed in a q-2D semi metal, namely, (TMTSF) 2 NO 3 under pressure.Among the members of the Bechgaard salts family, (TMTSF) 2 NO 3 exhibits numerous peculiar features. As the temperature decreases, an anion ordering (AO) transition with wave vector (1/2, 0, 0) is observed at ambient pressure at a temperature T AO ≃ 45 K [8,9] which remains independent of the magnetic field up to at least 36 T [10]. This leads to a q-2D FS with compensated electron and hole tubes [11]. At lower temperature, a SDW state with incommensurate wave vector and imperfect nesting is stabilized (T SDW = 9.1 K at ambient pressure) [12]. Under pressure higher than ∼ 8 kbar, the AO transition is shifted towards slightly higher temperatures [13] and a metallic state is stabilized at low temperature. Asymmetrical warping of the FS along the less conducting direction c* has been inferred from the absence of Yamaji features in the angular dependence of the magnetoresistance both in the SDW [14] and metallic [15] ...