Summary: We discuss the existence, uniqueness and stability exponential and polynomial of global solutions for a nonlinear coupled system with nonlocal boundary conditions given by \[ \begin{aligned} u_{tt}+\Delta^2u+f(u-v) & =0\text{ in }\Omega\times (0,\infty),\\ v_{tt}-\Delta v-f(u-v)& =0\text{ in }\Omega\times(0,\infty),\\ u=0 \text{ on }\Gamma_0\times(0, \infty),\;-u+\int^t_0g_1(t-s){\mathcal B}_2u(s)ds & =0 \text{ on }\Gamma_1 \times(0,\infty),\\ \frac{\partial u}{\partial\nu}=0,\text{ on }\Gamma_0 \times(0,\infty),\;\frac{\partial u}{\partial\nu}+\int^t_0g_2(t-s) {\mathcal B}_2u(s)ds& =0\text{ on }\Gamma_1\times(0,\infty),\\ v=0\text{ on } \Gamma_0\times(0,\infty),\;v+\int^t_0g_3(t-s)\frac{\partial v} {\partial \nu}(s)ds & =0\text{ on }\Gamma_1\times(0,\infty),\\ \bigl(u(0,x), v(0, x)\bigr)= \bigl(u_0 (x),v_0(x)\bigr),\;\bigl(u_t(0,x),v_t(0,x)\bigr)& = \bigl(u_1(x),v_1(x)\bigr) \text{ n }\Omega\end{aligned} \] where \(\Omega\) is a bounded region in \({\mathfrak R}^2\) whose boundary is partitioned into disjoint sets \(\Gamma_0,\Gamma_1\). We show that such dissipation is strong enough to produce uniform rate of decay. Besides, the coupled is nonlinear which brings up some additional difficulties, which makes the problem interesting.