  Let $f :\R\to\R$ be a continuous function. We prove that under some
additional assumptions on $f$ and $A:\R\to\R_{+}$, weak $\Cuno$ solutions of
the differential inequality $-\diver(A(\abs{\nabla u})\nabla u)\ge f(u)$ on
$\RN$ are nonnegative. Some extensions of the result in the framework of
subelliptic operators on Carnot Groups are considered.
