  We determine the subgroup of automorphisms acting trivially on the second
integral cohomology for hyperkaehler manifolds which are deformation equivalent
to O'Grady's sporadic examples. In particular, we prove that this subgroup is
trivial in the ten dimensional case and isomorphic to
$(\mathbb{Z}/2\mathbb{Z})^{\times 8}$ in the six dimensional case. Furthermore
we study the fixed loci of the automorphisms in the six dimensional case.
