  In this work we focus on entanglement of two--mode Gaussian states of
continuous variable systems. We first review the formalism of Gaussian measures
of entanglement, adopting the framework developed in [M. M. Wolf {\em et al.},
Phys. Rev. A {\bf 69}, 052320 (2004)], where the Gaussian entanglement of
formation was defined. We compute Gaussian measures explicitely for two
important families of nonsymmetric two--mode Gaussian states, namely the states
of extremal (maximal and minimal) negativities at fixed global and local
purities, introduced in [G. Adesso {\em et al.}, Phys. Rev. Lett. {\bf 92},
087901 (2004)]. This allows us to compare the {\em orderings} induced on the
set of entangled two--mode Gaussian states by the negativities and by the
Gaussian entanglement measures. We find that in a certain range of global and
local purities (characterizing the covariance matrix of the corresponding
extremal states), states of minimum negativity can have more Gaussian
entanglement than states of maximum negativity. Thus Gaussian measures and
negativities are definitely inequivalent on nonsymmetric two--mode Gaussian
states (even when restricted to extremal states), while they are completely
equivalent on symmetric states, where moreover the Gaussian entanglement of
formation coincides with the true one. However, the inequivalence between these
two families of continuous-variable entanglement measures is somehow limited.
In fact we show rigorously that, at fixed negativities, the Gaussian
entanglement measures are bounded from below, and we provide strong evidence
that they are also bounded from above.
