We study the behavior of solutions to the problem εu′′ε(t) +u′ε(t) +A(t)uε(t) =fε(t), t∈(0, T), uε(0) =u0ε, u′ε(0) =u1ε,in the Hilbert space H asε→0, whereA(t), t∈(0,∞),is a family of linear self-adjoint