When manufacturing hybrid components, especially the fan blades or stator vanes of an aircraft gas turbine including a metallic enveloping structure and a supporting structure in fiber-composite material, the mating faces of the metallic structure are cleaned and roughened with plasma prior to fitting the fiber-composite material and the metallic molecules activated so that high attractive forces take effect and an intimate, extremely strong adhesive connection is produced between the metal and the fiber-composite material. Fan blades or stator vanes of the fan structure of a gas-turbine engine which are manufactured according to this method are capable of transmitting high loads and feature a long service life.