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The phenomena of strong resonance occur due to dynamic modal interaction between the power system's modes when one/two system or controller parameters are varied. This study presents the effect of strong resonance while designing a single or multiple power system stabilisers (PSS) in multi-machine power systems that can lead to instability of the system. The effect of strong resonance is investigated in test and practical power systems. It is studied with full-order and reduced-order system models based on the method of perturbations suggested by Seiranyan. The authors also suggest a mechanism to mitigate strong resonance while tuning one or more PSS. The test systems considered are three-machine, ten-bus system and a four-machine, 11-bus practical system, a part of the southern-grid Indian power system.