Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the applications in structural dynamics, linear FRF matrices constructed from experimental measurements will not be complete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The validation of the method is demonstrated with case studies based on simulated experiments, as well as real experiments with two nonlinear structures. It is concluded in this study that the approach proposed improves the previously developed method by avoiding the use of footprint graphs in nonlinear identification and also by making it possible to identify more than one type of nonlinearity that may co-exist at the same location. (c) 2013 Elsevier Ltd. All rights reserved.