This present work investigates the NMR relaxation properties of a wide range of both healthy and leukaemic tissues to determine which tissues show the largest changes with disease development and to assess the timescale of these changes (white blood cell count was used to stage disease progression). The study makes use of a T-cell leukaemia animal model noted for its similarities to human lymphoblastic leukaemia animal studies of selected tissues assessed how well NMR changes related to pathological alterations in tissue structure and composition and identified possible causes for the observed NMR changes. Biochemical investigations were also performed to obtain a broader picture of the disease process. The sensitivity of another NMR technique known as Magnetization Transfer (MT) in the detection of leukaemic tissue changes was investigated. Various aspects of the instrumentation were developed, appropriate pulse sequences were written and suitable MT parameter settings for tissue experiments determined. Quantitative analysis of MT data was performed by fitting experimental results to a theoretical model for the MT process. Optimal MT parameter settings were established and the contribution of different processes to the MT effect were evaluated. Tissue postmortem NMR relaxation and MT properties were also investigated to determine the influence of postmortem measurement time in <I>in vitro</I> NMR results. Generally, it was found the NMR relaxation is more sensitive to disease development than MT. Liver showed the largest relaxation time changes although spleen showed the earliest significant changes. Therefore, tissues other than bone marrow show large NMR changes and would be worth investigating in a clinical environment. Also the different timescale of NMR changes between tissues may provide useful clinical information.