Amplitude and frequency dependences of intrinsic damping have been studied in copper-aluminum-nickel (Cu-Al-Ni) single crystals in the martensitic state after different heat treatments. The measurements of intrinsic damping were performed by resonant and forced oscillation techniques in a range from infra-to ultrasonic frequencies. The conclusion is drawn that during aging in β-phase (200°C) the behavior of the pinning obstacles in the martensitic state at room temperature changes from highly mobile and forming atmospheres around the mobile defects, presumably dislocations, to rather immobile and homogeneously distributed in the bulk of the crystal. Observed regularities of the amplitude-dependent intrinsic damping do not correspond to the breakaway model of amplitude-dependent internal friction both for quenched and aged specimens. In contrast to the generally accepted point of view, a notable frequency dependence of the amplitude-dependent damping is revealed, especially in the case of quenched specimens. Short-range pinning points are considered as basic obstacles for dislocation motion in the quenched specimens. Two types of obstacles are supposed to form the amplitude frequency spectra of damping for the aged specimens: purely hysteretic or athermal, due to the presence of γ-precipitates, and thermally activated due to the existence of short-range pinning points.