Abstract A procedure is presented for identifying the mechanical parameters of zero-memory non-linear discrete structural systems. The procedure allows both the parameter estimation of a priori known dynamical models as well as the identification of classes of suitable non-linear models based on input–output data. The method relies on a wavelet-based discretization of the non-linear governing differential equation of motion. Orthogonal Daubechies scaling functions are used in the analysis. The scaling functions localization properties permit the tracking of fast variations of the state of the dynamical system which may be associated with unmodeled dynamics of measurement noise. The method is based on the knowledge of measured state variables and excitations and applies to single and multi-degree-of-freedom systems under either free or forced vibrations.