  Let L be a Lagrangian submanifold of a pseudo- or para-K\"ahler manifold
which is H-minimal, i.e. a critical point of the volume functional restricted
to Hamiltonian variations. We derive the second variation of the volume of L
with respect to Hamiltonian variations. We apply this formula to several cases.
  In particular we observe that a minimal Lagrangian submanifold L in a
Ricci-flat pseudo- or para-K\"ahler manifold is H-stable, i.e. its second
variation is definite and L therefore a local extremizer of the volume with
respect to Hamiltonian variations. We also give a stability criterion for
spacelike minimal Lagrangian submanifolds in para-K\"ahler manifolds, similar
to Oh's stability criterion for minimal Lagrangian manifolds in
K\"ahler-Einstein manifolds.
  Finally, we determine the H-stability of a series of examples of H-minimal
Lagrangian submanifolds: the product of n circles of arbitrary radii in complex
space C^n is H-unstable with respect to any indefinite flat Hermitian metric,
while the product of n hyperbolas in para-complex vector space D^n is H-stable
for n=1,2 and H-unstable for n > 2. Recently, minimal Lagrangian surfaces in
the space of geodesics of three-dimensional space forms have been
characterized; on the other hand, a class of H-minimal Lagrangian surfaces in
the tangent bundle of a Riemannian, oriented surface has been identified. We
discuss the H-stability of all these examples.
