In this paper, we extend to a system of the type
\[
\begin{cases}
\begin{array}{c}
-\Delta_{p_{1}}u=f\left(v\right)\quad in\,\Omega,\quad u>0\quad in\,\Omega\quad u=0\quad on\,\partial\Omega,\\
-\Delta_{p_{2}}v=g\left(u\right)\quad in\,\Omega,\quad v>0\quad in\,\Omega\quad v=0\quad on\,\partial\Omega,
\end{array}\end{cases}
\]
where $\Omega\subset\mathbb{R}^{N}$ is bounded, the monotonicity
and simmetry results of Damascelli and Pacella obtained in $\left[5\right]$
in the case of a scalar p-Laplace equation with 1 < p < 2. For this
purpose, we use the moving hyperplanes method and we suppose that
$f,g\::\:\mathbb{R}\rightarrow\mathbb{R}^{+}$ are increasing on $\mathbb{R}^{+}$
and locally Lipschitz continuous on $\mathbb{R}$ and p$_{1},$ p$_{2}$
$\epsilon$ (1, 2) or p$_{1}\:\epsilon\left(1,\infty\right),$ p$_{2}$=2
