Abstract: Single-crystal components of gas turbine engines, like turbine blades, are inspected in the installed state within the engine for cracking in certain critical areas using longitudinal ultrasonic waves. A first, rough orientation of the ultrasonic waves onto the critical area is accomplished under camera-visual control using an ultrasonic probe whose shape conforms to the respective component area and which, therefore, can be form-fitted to the component. For fine-positioning of the ultrasonic waves in the critical area, a reference signal is generated at a component-specific geometrical contour adjacent to the critical area by second ultrasonic waves emitted at a local distance to the first ultrasonic waves. The presence of this signal ensures the safe, disturbance-free detection of cracks in the critical blade area by means of longitudinal sonic waves. The invention includes an apparatus for the performance of the method.