  We generalize the notions of the Futaki invariant and extremal vector field
of a compact K\"ahler manifold to the general almost-Kahler case and show the
periodicity of the extremal vector field when the symplectic form represents an
integral cohomology class modulo torsion. We also give an explicit formula of
the hermitian scalar curvature in Darboux coordinates which allows us to obtain
examples of non-integrable extremal almost-K\"ahler metrics saturating LeBrun's
estimates.
