We consider the system $ẋ\left(t\right)-\int {₀}^{\eta }dR̃\left(\tau \right)ẋ(t-\tau )={\int }_0^{\eta }dR\left(\tau \right)x(t-\tau )+\left[Fx\right]\left(t\right)+u\left(t\right)$ (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...