  In this paper we study the Liouville-type properties for solutions to the
steady incompressible Euler equations with forces in $\Bbb R^N$. If we assume
"single signedness condition" on the force, then we can show that a $C^1 (\Bbb
R^N)$ solution $(v,p)$ with $|v|^2+ |p|\in L^{\frac{q}{2}}(\Bbb R^N)$, $q\in
(\frac{3N}{N-1}, \infty)$ is trivial, $v=0$. For the solution of of the steady
Navier-Stokes equations, satisfying $v(x)\to 0$ as $|x|\to \infty$, the
condition $\int_{\Bbb R^3} |\Delta v|^{\frac65} dx<\infty$, which is stronger
than the important D-condition, $\int_{\Bbb R^3} |\nabla v|^2 dx <\infty$, but
both having the same scaling property, implies that $v=0$. In the appendix we
reprove the Theorem 1.1(\cite{cha0}), using the self-similar Euler equations
directly.
