  In this note we prove local regularity results for distributional solutions
and subsolutions of semilinear elliptic systems such as $$ L_k^m u_k =
f_k(x,u_1,\ldots,u_N) \quad\text{in }\mathbb{R}^n\qquad (k=1,\ldots,N) $$ where
$L_1,\ldots,L_N$ are of divergence-form and $n\geq 2m$. We show that
distributional subsolutions are locally bounded from above if $|f_k(x,z)|\leq
C(1+|z|^p)$ for $1\leq p<\frac{n}{n-2m},k=1,\ldots,N$.
  Furthermore, regularity properties of subsolutions and improved versions for
bounded subsolutions are given. Even for $f_1=\ldots=f_N=0$ our results are
new.
