A generic adaptive approach is proposed for diagnosis of the bilinear mechanical systems. The approach adapts the free oscillation method for bilinearity diagnosis of mechanical systems. The expediency of the adaptation is proved for a recognition feature, the decrement of the free oscillations. The developed adaptation consists of variation of the adaptive likelihood ratio of the decrement with variation of the resonance frequency of the bilinear system. It is shown that in the cases of the frequency-independent and the frequency-dependent internal damping, the adaptation is expedient. To investigate effectiveness of the adaptation in these cases, a numerical simulation was carried out. The simulation results show that use of the adaptation increases the total probability of the correct diagnosis of system bilinearity.