  The first part of this article is devoted to the study families of totally
real intersecting $n$-submanifolds of $(\Bbb C^n,0)$. We give some conditions
which allow to straighten holomorphically the family. If this is not possible
to do it formally, we construct a germ of complex analytic set at the origin
which interesection with the family can be holomorphically staightened. The
second part is devoted to the study real analytic $(n+r)$-submanifolds of
$(\Bbb C^n,0)$ having a CR-singularity at the origin ($r$ is a nonnegative
integer). We consider deformations of quadrics and we define generalized Bishop
invariants. Such a quadric intersects the complex linear manifold
${z_{p+1}=...=z_n=0}$ along some real linear set ${\cal L}$. We study what
happens to this intersection when the quadric is analytically perturbed. On the
other hand, we show, under some assumptions, that if such a submanifold is
formally equivalent to its associated quadric then it is holomorphically
equivalent to it.
  All these results rely on a result stating the existence (and
caracterization) of a germ of complex analytic set left invariant by an abelian
group of germs of holomorphic diffeomorphisms (not tangent to the identity at
the origin).
