Let $k$ be a field of characteristic 0 and $G$ a linear algebraic $k$-group. When $G$ is abelian, it is well known that torsors under $G_{X}$ over a $k$-scheme $\\pi:X\\to \\textup{Spec} k$ provide an obstruction to the existence of $k$-rational points on $X$, since Leray spectral sequence gives rise (when $X$ is \'nice\', e.g. $X$ smooth and proper) to an exact sequence of groups (5-term exact sequence associated). This sequence gives an obstruction for a $\\bar{G}_{X}$-torsor $\\bar{P}\\to\\bar{X}$ with field of moduli $k$ to be defined over $k$, i.e. to be obtained by extension of scalars to the algebraic closure $\\bar{k}$ of $k$ from a $G_{X}$-torsor $P\\to X$. This obstruction is measured by a gerbe, which is neutral if $X$ possesses a $k$-rational point. We try to extend this result to the non-commutative case, and in some cases, we deduce non-abelian cohomological obstruction to the existence of $k$-rational points on $X$, and results about descent of torsors.