Using Dirac's approach to constrained dynamics, the Hamiltonian formulation
of regular higher order Lagrangians is developed. The conventional description
of such systems due to Ostrogradsky is recovered. However, unlike the latter,
the present analysis yields in a transparent manner the local structure of the
associated phase space and its local sympletic geometry, and is of direct
application to {\em constrained\/} higher order Lagrangian systems which are
beyond the scope of Ostrogradsky's approach.