  We provide a class of inequalities whose violation shows the presence of
entanglement in two-mode systems. We initially consider observables that are
quadratic in the mode creation and annihilation operators and find conditions
under which a two-mode state is entangled. Further examination allows us to
formulate additional conditions for detecting entanglement. We conclude by
showing how the methods used here can be extended to find entanglement in
systems of more than two modes.
