The authors derive an equation of the Lippmann-Schwinger type for a pair of self-adjoint operators \(A,\widetilde{A}\), where \(\widetilde{A}\) is a singular perturbation of \(A\) defined by the Krein resolvent formula. A heuristic formula for a solution is given, which is then rigorously justified for various situations – rank one singular perturbations, generalized Schrödinger operators \(-\Delta +\mu\), where \(\mu\) is a measure supported by a null set.