  The third unramified cohomology group is shown to vanish on certain varieties
equipped with a pencil of quadrics or of smooth complete intersections of two
quadrics. Over the complex field, this shows that the integral Hodge conjecture
in degree 4 holds for such varieties.
  ---
  On \'etablit la nullit\'e du troisi\`eme groupe de cohomologie non ramifi\'ee
pour certaines vari\'et\'es munies d'un pinceau de quadriques ou
d'intersections compl\`etes lisses de deux quadriques. Sur les complexes, ceci
permet d'\'etablir la conjecture de Hodge enti\`ere en degr\'e 4 pour de telles
vari\'et\'es.
