  A universal lower bound for the first positive eigenvalue of the Dirac
operator on a compact quaternionic Kaehler manifold M of positive scalar
curvature is calculated. It is shown that it is equal to the first positive
eigenvalue on the quaternionic projective space. For this, the horizontal
tangent bundle on the canonical SO(3)-bundle over M is equipped with a
hyperkaehlerian structure and the corresponding splitting of the horizontal
spinor bundle is considered. The desired estimate is obtained by looking at
hyperkaehlerian twistor operators on horizontal spinors.
