Although the identification and analysis of structures with a localized nonlinearity, either weak or strong, is within reach, identification of multiple nonlinearities coexisting at different locations is still a challenge, especially if these nonlinearities are strong. In such cases, identifying each nonlinearity separately requires a tedious work or may not be possible at all in some cases. In this paper, an approach for experimental modal analysis of nonlinear systems by using Response-Controlled stepped-sine Testing (RCT) is proposed. The proposed approach is applicable to systems with several nonlinearities at various different locations, provided that modes are well separated and no internal resonances occur. Step-sine testing carried out by keeping the displacement amplitude of the driving point constant yields quasi-linear frequency response functions directly, from which the modal parameters can be identified as functions of modal amplitude of the mode of concern, by employing standard linear modal analysis tools. These identified modal parameters can then be used in calculating near-resonant frequency response curves, including the unstable branch if there is any, for various untested harmonic forcing cases. The proposed RCT approach makes it also possible to extract nonlinear normal modes experimentally without using sophisticated control algorithms, directly from the identified modal constants, and also to obtain near-resonant frequency response curves experimentally for untested constant-amplitude harmonic forcing cases by extracting isocurves of constant-amplitude forcing from the measured Harmonic Force Surface (HFS), a new concept proposed in this paper. The key feature of the HFS is its ability to extract unstable branches together with turning points of constant-force frequency response curves directly from experiment, accurately. The method is validated with numerical and experimental case studies. The numerical example consists of a 5 DOF lumped system with strong several conservative nonlinear elements. Experimental case studies consist of a cantilever beam supported at its free-end by two metal strips which create strong stiffening nonlinearity, and a real missile structure which exhibit moderate damping nonlinearity mostly due to several bolted joints on the structure. (C) 2020 Elsevier Ltd. All rights reserved.