When a downstream circular cylinder is in the vicinity of the disturbed wake flow which is originated from the presence of an upstream cylinder, fluid-structure interactions due to vortex- and wake-induced vibrations may coexist. Their combined effects are of practical concern for offshore structures deployed in an array or proximity such as marine risers, pipelines and mooring lines. The wake flow deficit law and wake-induced drag and lift hydrodynamic forces are modelled based on the boundary layer theory, which is modified to account for the oscillation of the upstream cylinder. Unsteady drag and lift forces associated with the vortex-induced vibration (VIV) and wake-induced vibration (WIV) are represented dynamically by van der Pol-type wake oscillators. The present paper proposes a new modelling concept and framework capable of evaluating the combined WIV-VIV of tandem circular cylinders in comparison with experimental data, capturing a key feature of the wake stiffness associated with WIV. An equivalent natural frequency based on the wake stiffness mechanism behaves equivalently to the WIV frequency. Numerical studies show that the downstream cylinder may respond in a multi-frequency scenario at specific reduced velocities. The prediction model captures the wake stiffness trend similar to the experimental observation. The correlation to the wake stiffness concept allows the identification of situations for which the downstream cylinder is mainly governed by the WIV mechanism resulting in largest vibration amplitudes.