Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if X = ∩ i = 1 r D i ⊂ G / P is a smooth complete intersection of r ample divisors such that K G / P ∗ ⊗ O G / P (- ∑ i D i) is ample, then X is Fano. We first classify these Fano complete intersections which are locally rigid. It turns out that most of them are hyperplane sections. We then classify general hyperplane sections which are quasi-homogeneous.