The author considers the following nonlinear parabolic equations of the reaction diffusion type \[ {\partial u\over\partial t}-\sum_{i=1}^{n}{\partial\over\partial x_i}\Biggl(\biggl|{\partial u\over\partial x_i}\biggr|^{p-2}{\partial u\over\partial x_i}\Biggr)+ f_1(u)-f_2(u)\ni h, \quad \text{in} \Omega\times (0,\infty),\quad u|_{\partial \Omega}=0,\quad u|_{t=0}=u_0, \] where \(p\geq 2,\) \(\Omega\subset {\mathbb R}^n, \) \(h\in L_2(\Omega),\) and \(f_i:{\mathbb R}\to 2^{\mathbb R},\) \(i=1,2,\) are maximal monotone maps. It is studied the existence of global compact attractors for the above equations without uniqueness of the solutions.