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The use of discrete damping devices in New Zealand buildings is increasing as designers seek to limit damage to both architectural and structural building elements in moderate earthquakes. The overall damping of the structure becomes a combination of inherent material damping, hysteretic damping from yielding of building elements at specific locations and damping from discrete devices. For over 60 years, engineers have used simplified analysis procedures (e.g., modal response spectrum analysis) to predict building response under seismic actions. The design of structures incorporating viscous dampers requires a paradigm shift in approach as the force each damper resists is a function of the relative velocity between its ends. Popular pseudo-static design methodologies promote the use of a viscous strut in the analysis model to represent them. However, it is incorrect to use elastic, mode-based analysis for a structure incorporating damping devices and relying on significant inelastic behaviour. This paper elucidates the complex mechanics of damper-structure interaction by reviewing some of the established classical, modal-based, simplified analysis techniques used in seismic design. A series of numerical investigations demonstrate how these techniques are usually invalid for structures that incorporate viscous dampers because they violate the laws of physics. The reason why mode-based techniques are invalid is explored with reference to the imaginary components of the natural modes of vibration and the effect on them of significant inelasticity within the structure. The dynamic characteristics of viscous dampers challenge conventional design approaches such as displacement-based design. This paper establishes that nonlinear time-history analysis is the only meaningful way of predicting the dynamic response of a structure incorporating viscous dampers when significant inelastic behaviour of the structure is expected. [ABSTRACT FROM AUTHOR]