Selective damping apparatus comprises at least one sensor (7) for detecting, and producing signals indicative of at least the frequency and amplitude of vibrations of a first structural component ("the resonant structure") (6) having one or more resonant frequencies, at least one vibration generator (40) for generating damping vibrations for application to the resonant structure, a controller (8) for controlling the operation of the vibration generator (40) in delayed response to the signals produced by the at least one sensor (7), and wherein at least one of said at least one sensor (7) and of said at least one vibration generator (40) is adapted to operate in co-operation with a second structural component ("the non-resonant structure") (2) relatively insensitive to the resonant frequencies of the resonant structure (6) and connected or coupled to said resonant structure (6) either directly or indirectly via one or more intermediate structural components.