  We prove an equivariant deformation result for Hamiltonian stationary
Lagrangian submanifolds of a Kahler manifold, with respect to deformations of
its metric and almost complex structure that are compatible with an isometric
Hamiltonian group action. This yields existence of Hamiltonian stationary
Lagrangian submanifolds in possibly non-Kahler symplectic manifolds whose
metric is arbitrarily close to a Kahler metric.
