The present invention relates to an apparatus for machining holes, especially to machine holes in a surface of a coated gas turbine airfoil, which apparatus comprises a laser device for laser drilling and an electrode for electrical discharge machining. Further the invention relates to a method to machine a hole into a coated surface with an apparatus of the incipiently mentioned type. Known methods make use of a machine with separate machine heads for laser drilling and electrical discharge machining. By combining these two devices in one machine head the invention gives the possibility to save time and obtain very accurate results.