Mass-spring and liquid dampers enable structural vibration control to attenuate single, coupled lateral and torsional vibrations in diverse structures. Out of these, the passively tuned liquid damper (TLD) class is wanted due to its broad applicability, extreme reliability, robustness, long life time and ease of manufacturability. In this PhD thesis, the theory, design, verification and validation of multi-mode TLDs in terrestrial and mainly spacecraft (S/C) applications have been studied. The most challenging TLD design of the type “tube-with-endpots” was the Chinese meteorological FY-2 S/C nutation damper in the 90s. The extreme performance requirements like the 0.5” residual nutation damping angle implied an extended test program which led to refined insights in the recursive calibration method and limiting damping performance. The test analysis results and the involvement in the in-orbit analysis of the Ulysses S/C nutation anomaly in the same period, led the author to the idea of a multi-mode TLD system. The concept was proposed and successfully applied in the Cluster S/C for the effective damping of both nutation and coupled wire boom (antenna) oscillation modes. To come that far, the essentials of spacecraft dynamics and its control required an extension of the liquid flow models and an appropriate TLD design methodology to include multi-mode excitations. The TLD key performance parameters are the dissipation rate, residual damping angle and the resonance frequency which is directly related to the effective damping length. This parameter used to be obtained by an educated guess on basis of test heritage. The existing practical design rules, however, were overruled by new insights which are based on the latest scientific results from fluid mechanics. This knowledge and the extensive analysis of all available TLD damping performance tests resulted in a new refined methodology to estimate the effective damping length properly. The eventual value, however, must still be determined via recursive calibration cycles but better initial estimates reduce the required test times significantly. The residual damping angle is limited by the TLD endpot behavior which is determined by the physics of the liquid meniscus interaction with the endpot wall. Though the TLD design is characterized by a very low residual angle with almost zero dead-band, the very limit is not clear. This issue was investigated using multiple models and experiments whilst the state-of-the-art in the scientific literature from nano-tribology and wetting transitions on biomimetic surfaces was explored. Test refinements are proposed to decrease damping fluctuations and extend the low angular test range. Although, the limiting angle is not known, there is strong evidence that the limits can be extended beyond the 0.1” flight value. The early design phase of the broadband Cluster TLDs in 1991 and the TLD developments up to 2012 were studied. Moreover, the spin-stabilized magneto-spherical S/C Bepi-Colombo, Cluster, RBSP, DICE, Themis and FAST are compared which confirm the applicability of the multi-mode TLD concept. The study of the generic theory of wire boom oscillations, gyroscopically coupled to the S/C hub spin and nutation modes, resulted in a new harmonized parameterization and derived equations. The Cluster TLD system with in addition the internal wire boom damping enable the boom deflection limit and its damping time constant to be design parameters. On basis of this knowledge, a recursive bottom-up TLD design methodology was developed. The stability study including the wire boom composition made clear where the limit of multi-mode modeling is reached and breadboard experiments and practical engineering trade-offs are required. The optimal wire boom deployment strategy using the multi-mode damping principle was analyzed. At small angular deflections, however, material artifacts and anelastic flexure dominate and only dedicated engineering tests can clarify these issues. The current status of the TLD design was investigated by comparing the RBSP S/C [2012] ring TLD and the Cluster S/C [2000] endpot TLD designs. The combination of the Cluster TLD bottom-up design methodology with the 9 degrees of freedom RBSP top-down model completed the model base for the design of multi-mode TLDs in flexible S/C. The RBSP TLD suffers with considerable angular off-sets and inrush time constants which are not accounted for in the RBSP model. The Cluster TLD design, however, lacks these artifacts. RBSP S/C flight validation data, however, are not yet available. The nutation related Cluster flight data validate the TLD model predictions firmly within the requirements. This renders an indirect but incomplete prove of the effectiveness of the TLD system design. It is hard, however, to trace and validate the designed multi-mode performance itself. It is, therefore, of great scientific value to obtain Attitude Determination and Control System flight data. A successful TLD development requires risk mitigation as an essential part of systems engineering (SE). An inventory of boundary conditions was made thinking ahead for production and project cost escalations. In the high-tech industry, however, there is little focus on a scientifically based bottom-up SE approach though such effort does pay off. It was one of the quests of this thesis to prove the added value of such an investment. As a result, the developed methodologies do contribute to a profound SE approach in the development of multi-mode TLDs. The space qualified broadband TLD design with endpots is an excellent choice for use in future spin-stabilized S/C with wire boom configurations. The results of the PhD thesis enable the extreme refinement of the given damper concept. Market research and the allocation of dedicated solutions are a way towards valorization. Terrestrial spin-offs in the engineering fields of refined (ultra) centrifuges, pulsating industrial piping systems, windmills, earthquake control of building structures, shipbuilding and bridge stabilization offer the best valorization opportunities in short terms.