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This thesis describes water proton and deuterium relaxation processes, as seen by Nuclear Magnetic Resonance (NMR) spectroscopy, using Brownian Dynamics (BD) or Molecular Dynamics (MD) simulations. The MD simulations reveal new detailed information about the dynamics and order of water molecules outside of a lipid bilayer. This is very important information in order to fully understand deuterium NMR measurements in lipid bilayer systems, which require an advanced analysis, because of the complicated water motion (such as tumbling and self-diffusion). The BD simulation methods are combined with the powerful Stochastic Liouville Equation (SLE) in its Langevin form (SLEL) to give new insight into both ¹H₂O and ²H₂O relaxation. The new simulation techniques which combine BD and SLEL can give important new information in cases where other methods do not apply. The deuterium relaxation is described in the context of a water/lipid interface and is in a very elegant way combined with the simulation of diffusion on curved surfaces developed by our research group. ¹H₂O spin-lattice relaxation is described for paramagneticsystems. With this we mean systems with paramagnetic transition metal ions or complexes, that are dissolved into a water solvent. The theoretical description of such systems are quite well investigated but such systems are not yet fully understood. An important consequence of the Paramagnetic Relaxation Enhancement (PRE) calculations when using the SLEL approach combined with BD simulations is that we obtain the electron correlation functions, which describe the relaxation of the paramagnetic electron spins. This means for example that it is also straight forward to generate Electron Spin Resonance (ESR) lineshapes.