The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system $ i \partial_t E+\nabla (\nabla . E)-\alpha^2 \nabla \times \nabla \times E =-|E|^{2\sigma}E, $ where $E:{\ensuremath{{\Bbb R}}}^3\rightarrow{\mathbb C}^3$. This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L ²-subcritical σ (that is σ ≤ 2/3) and the H ¹-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the $H^1({\ensuremath{{\Bbb R}}}^3)$ norm.