  We characterize HKT structure in terms of nondegenrate complex Poisson
bivector on hypercomplex manifold. We extend the characterization to the
twistor space. After considering the flat case in detail, we show that the
twistor space of hyperkaehler manifold admits a holomorphic Poisson structure.
We briefly mention the relation to quaternionic and hypercomplex deformations
on tori and K3 surfaces
