In the paper is studied the asymptotic behaviour, as \(t\to \infty\), of global bounded solutions of the second order semilinear evolution problem \[ \begin{aligned} &u_{tt}+\alpha u_t=\Delta u+f(x,u)\quad \text{in } \mathbb{R}^+\times \Omega\\ &u=0\quad \text{on } \mathbb{R}^+\times \partial \Omega, \tag{1}\\ &u(0,\cdot)=u(\cdot), \quad u_t(0,\cdot)=u(\cdot)\quad \text{in } \Omega,\end{aligned} \] where \(\Omega\) is a bounded smooth domain of \(\mathbb{R}^N, \alpha >0\) and \(f:\Omega \times \mathbb{R}\to \mathbb{R}\) is a smooth function. Assume that \(f(x,s)\) is analytic in \(s\), \(f(x,s), \frac{\partial f}{\partial s}(x,s), \frac{\partial ^2f}{\partial s^2}(x,s)\) are bounded in \(\Omega\times (-\beta,\beta)\), for all \(\beta>0\). Under this conditions the author proves that there exists \(p\geq 2\) such that \(\bigcup_{t\geq 0} \{u(t,\cdot),u(t,\cdot)\}\) is precompact in \(W^{2,p}(\Omega)\times W^{1,p}(\Omega)\), with \(p>N/2\) if \(N\leq 6\), and \(p>N\) if \(N>6\). Moreover, there exists \(\phi\in H^2(\Omega) \cap H^1_0(\Omega)\) with \(-\Delta \phi=f(x,\phi)\) in \(\Omega\) such that \[ \lim_{t\to +\infty} (\| u_t(t,\cdot)\|_{L^2(\Omega)}+ \| u(t,\cdot)-\phi(\cdot)\|_{W^{2,p}(\Omega)})=0. \] Let \(V\subset H=L^2(\Omega,\mathbb{R}^d)\) be a real Hilbert space, such that \(V\) is dense in \(H\) and the imbedding of \(V\) in \(H\) is compact. Let \(A\) be a linear unbounded self-adjoint operator associated with a bilinear continuous, symmetric and coercive form \(a(u,v)\) on \(V\), and \(B\) is a linear bounded operator \(B:H\to H\) such that \((Bx,x)_H\geq \alpha\| x\|_H\), \(\alpha>0\). Under suitable conditions on operators \(A, B\) and function \(f, f:A^{-1}(L^p(\Omega, \mathbb{R}^d))\to L^p(\Omega,\mathbb{R}^d)\) the author generalizes the result obtained for the problem (1) for the following problem: \[ u_{tt}+Bu_t+Au=f(x,u),\qquad u(0,\cdot)=u_0(\cdot),\quad u_t(0,\cdot)=u_1(\cdot). \]