In this work we study the existence, uniqueness and decay of solutions to a class of viscoelastic equations in a separable Hilbert space $H$given by $$\begin{array}{c}{u}_{tt}+M\left(\left[u\right]\right)Au-{\int }_0^{t}g(t-\tau )N\left(\left[u\right]\right)Aud\tau =0,\text{in}{L}^2(0,T;H)\\ u\left(0\right)=u_0,u_t\left(0\right)=u_1\end{array}$$ where by$\left[u\left(t\right)\right]$we are denoting $$\left[u\left(t\right)\right]=\left((u\left(t\right),u_t\left(t\right),(Au\left(t\right),u_t\left(t\right)),\parallel A^{\frac{1}{2}}u\left(t\right){\parallel }^2,\parallel A^{\frac{1}{2}}{u}_t\left(t\right){\parallel }^2,\parallel Au\left(t\right){\parallel }^2\right)\in {ℝ}^5$$