Abstract: To drill small holes in a metal component having a non-conductive, e.g. ceramic, surface layer apparatus is provided capable of carrying out both ultrasonic and EDM drilling operations without dismounting the component. The drilling operation commences with an ultrasonic drilling phase and change over to essentially EDM operation when breakthrough of the ceramic surface layer is detected. Breakthrough is detected by applying a low voltage pulse signal to a drilling electrode and sensing when current starts to flow between the electrode and the workpiece. When a multiplicity of holes are drilled simultaneously the changeover to EDM is triggered by breakthrough of the first electrode but may be delayed to permit the remaining electrodes to breakthrough.