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The spin-dynamics of Fermi-liquid helium-3 in pure form and in its mixtures with helium-4 are considered in this thesis. A linearised model of the spin dynamics is developed from Leggett’s equation of motion, including spin-diffusion, the Leggett-Rice spin-rotation effect and cylindrical boundary conditions. The equations are solved using a matrix formalism, allowing simulation of FIDs, NMR spectra and spin-echoes. The boundary conditions are shown to cause deviations of spin-echo amplitude and phase from the predictions of Leggett and Rice, for realistic experi-ments. The model is extended to include the demagnetising field (dipolar field) due to the magnetisation of the sample itself. Simulations show that, when the demag-netising field is strong, spectral clustering is present and sharp peaks are observed in the NMR spectrum. Data from NMR experiments on 3He and 3He-4He mixtures in an 11.3T mag-netic field, performed in Nottingham in 1999/2000, are analysed. The analysis of 6.2 % 3He mixture is predominantly by least-squares fitting of the model (excludin