This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 × H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(Ω2) × H1(Ω).The finite dimensionality of the global attractor is also established.