  In this paper we study the existence of solution for the following class of
system of elliptic equations $$
  \left\{
  \begin{array}{lcl}
  -\Delta u=\left(a-\int_{\Omega}K(x,y)f(u,v)dy\right)u+bv,\quad \mbox{in}
\quad \Omega
  -\Delta v=\left(d-\int_{\Omega}\Gamma(x,y)g(u,v)dy\right)v+cu,\quad \mbox{in}
\quad \Omega u=v=0,\quad \mbox{on} \quad \partial\Omega
  \end{array}
  \right.
  \eqno{(P)}
  $$ where $\Omega\subset\R^N$ is a smooth bounded domain, $N\geq1$, and
$K,\Gamma:\Omega\times\Omega\rightarrow\R$ is a nonnegative function checking
some hypotheses and $a,b,c,d\in\R$. The functions $f$ and $g$ satisfy some
conditions which permit to use Bifurcation Theory to prove the existence of
solution for $(P)$.
