<p>This work explores the response of systems with concentrated stiffness or damping nonlinearities and related features including detached resonances/isolas, Limit Cycle Oscillations (LCO) and frequency lock-in regions. To this end we propose a novel concept of Frequency Response (FR) boundary, which is obtained by parameter sweeps in a linearized model of the system. The FR boundary is then combined with the appropriate Describing Function (DF) of the nonlinearity to arrive at the final response. The forced response without LCO is obtained and its stability is determined using the harmonic DF and Incremental Input DF available in the literature. Whereas the forced response with coexisting LCO is computed with the aid of a ‘Constrained Harmonic DF’ derived by the author. Results are presented for multiple degrees of freedom systems as well as for the Duffing and Van der Pol oscillators. Stable and unstable systems are respectively addressed using DFs with one and two base frequencies, and these results are confirmed via time marching simulations. Interesting insights and simple explanations are provided regarding the distinctive features of inner and outer isolas, LCO quenching/entrainment and lock-in boundaries. The proposed method thus extends established control theory tools, namely multi-input DFs, into structural dynamics areas where nonlinearities are restricted to one spatial or generalized coordinate.</p>