Dynamic characteristics of structures in operational conditions are commonly identified from measured responses using Operational Modal Analysis (OMA). The OMA techniques are, however, confined to the principle of linearity. To overcome some of this limitation, this paper proposes a method for an OMA-based conditional linear approximation of a type of nonlinear systems, by which two or more sets of linear modes are estimated that together describe the behaviour of the true system. These sets of modes can be used to update a nonlinear numerical model that fits each linear estimate in relation to the associated conditions. Additionally, the method can alleviate the issue of varying approx. natural frequencies of nonlinear systems, when employing Structural Health Monitoring to detect damages based on changes of these. The method is demonstrated on both a numerical and an experimental study. Specifically, the numerical study consists of a cantilever beam with a clearance and a stopper at the tip, and it is shown, based on a single response measurement with multiple channels, that the method enables identification of both the underlying linear system and a linear system with modal properties affected by the nonlinearity. The experimental study consists of two simple, friction-coupled, offshore platform-like models, for which two sets of modes are estimated from one measurement, each set characterising the dynamic behaviour in coupled and uncoupled state, respectively. The paper also demonstrates that the proposed method can relieve the said complications of conducting Structural Health Monitoring of structures with changing natural frequencies due to nonlinearity.