It is shown that the operators associated with the perturbed wave equation in ℝn and with the elliptic operators with an indefinite weight function and mildly varying coefficients on ℝn are similar to a selfadjoint operator in a Hilbert space. These operators have the whole ℝ as the spectrum. It is shown that they are positive operators in corresponding Krein spaces, and the whole problem is reduced to showing that 0 is not a signular critical point.