  We study nonlinear systems of the form
$-\Delta\_pu=v^{q\_1}+\mu,\;-\Delta\_pv=u^{q\_2}+\eta$ and
$F\_k[-u]=v^{s\_1}+\mu,\;F\_k[-v]=u^{s\_2}+\eta$ in a bounded domain $\Omega$
or in $\mathbb{R}^N$ where $\mu$ and $\eta$ are nonnegative Radon measures,
$\Delta\_p$ and $F\_k$ are respectively the $p$-Laplacian and the $k$-Hessian
operators and $q\_1$, $q\_2$, $s\_1$ and $s\_2$ positive numbers. We give
necessary and sufficient conditions for existence expressed in terms of Riesz
or Bessel capacities.
