In a real Hilbert space H we consider the following singularly perturbed Cauchy problem {_εu′′ εδ^{(t) +δ u′}εδ^{(t) +Au}εδ(t) + B⁽u_εδ (t)⁾ = f(t), t ∈ (0, T ), u_εδ (0) = u₀, u^′εδ^{(0) =u}1, where u₀, u₁ ∈ H, f: [0, T ] ↦→ H, ε, δ are two small parameters, A is a linear self-adjoint operator and B is a nonlinear A^1/2 Lipschitzian operator. We study the behavior of solutions u_εδ in two different cases: ε → 0 and δ ≥ δ₀ > 0; ε → 0 and δ → 0, relative to solution to the corresponding unperturbed problem. We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0.