In a real Hilbert space $H$ we consider the following singularly perturbed Cauchy problem $\varepsilon\,u''_{\varepsilon\delta}(t)+ \delta\,u'_{\varepsilon\delta}(t)+Au_{\varepsilon\delta}(t)+B(u_{\varepsilon\delta}(t))= f(t),\quad t\in(0,T),\,\, u_{\varepsilon\delta}(0)=u_0,\,\,u'_{\varepsilon\delta}(0)=u_1,$   where $u_0, u_1\in H$, $f:[0,T]\mapsto H,$ $\varepsilon,$ $\delta$ are two small parameters, $A$ is a linear self-adjoint operator and $B$ is a nonlinear lipschitzian operator. We study the behavior of solutions $u_{\varepsilon\delta}$ in two different cases: $\varepsilon\to 0$ and $\delta \geq \delta_0>0;$ $\varepsilon\to 0$ and $\delta \to 0,$ relative to solution to the corresponding unperturbed problem.

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