  In this paper we prove Liouville type result for the stationary solutions to
the compressible Navier-Stokes-Poisson equations(NSP) and the compressible
Navier-Stokes equations(NS) in $\Bbb R^N$, $N\geq 2$. Assuming suitable
integrability and the uniform boundedness conditions for the solutions we are
led to the conclusion that $v=0$. In the case of (NS) we deduce that the
similar integrability conditions imply $v=0$ and $\rho=$constant on $\Bbb R^N$.
This shows that if we impose the the non-vacuum boundary condition at spatial
infinity for (NS), $v\to 0$ and $\rho\to \rho_\infty >0$, then $v=0$,
$\rho=\rho_\infty$ are the solutions.
