  The nuclear incompressibility $\kappa$ is investigated in asymmetric systems
in a mean field model. The calculations are done at zero and finite
temperatures and include surface, Coulomb and symmetry energy terms for several
equations of state. Also considered is the behavior of the incompressibility at
constant entropy $kappa_Q$ which is shown to have a very different behavior
than the isothermal $kappa$. Namely, $kappa_Q$ decreases with increasing
entropy while the isothermal $kappa$ increases with increasing $T$. A duality
is found between the adiabatic $kappa_Q$ and the T=0 isothermal $kappa$.
Analytic and also simple approximate expressions for $kappa$ are given.
