  In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable $z$ depending on n
parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new
canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates.
