P.Jonas and H.Langer [J. Oper.Theory 2, 63–77 (1979; Zbl 0478.47020)] showed that a definitizable operator in a Krein space remains definitizable after a finite-dimensional perturbation (in the sense of the resolvent) if the perturbed operator is selfadjoint and has a nonempty resolvent set. The present paper generalizes this result to a class of selfadjoint operators in Krein spaces which locally have the same spectral properties as definitizable operators, and it applies the generalized result to the study of the spectral properties of direct sums of indefinite Sturm–Liouville operators.