  The main purpose of the paper is to study hyperkahler structures from the
viewpoint of symplectic geometry. We introduce a notion of hypersymplectic
structures which encompasses that of hyperkahler structures. Motivated by the
work of Kronheimer on (co)adjoint orbits of semi-simple Lie algebras, we define
hyper-Lie Poisson structures associated with a compact semi-simple Lie algebra
and give criterion which implies their existence. We study an explicit example
of a hyper-Lie Poisson structure, in which the moduli spaces of solutions to
Nahm's equations assocaited to Lie algebra $\frak{su}(2)$ are realized as
hypersymplectic leaves and are related to the (co)adjoint orbits of
$\frak{sl}(2, \complex)$.
