This work describes the study of magneto-hydro-dynamic instabilities (MHD) commonly observed in plasma discharges in tokamak TCABR (at Instituto de Física da USP). Two main diagnostics were employed to observe these instabilities: a poloidal set of 24 magnetic coils (Mirnov coils) placed near the plasma border and a detector of emissions in the Ultra Violet and soft X-ray range with 20 channels (SXR system) which improvement of the signal conditioning circuit was done as part of this work. These diagnostics were chosen because they provide complementary information, since the SXR system measures the central part of the plasma column, while the Mirnov coils detect the MHD instabilities in the outer part of the column. The information collected by these diagnoses was submitted to spectral analysis with temporal and spatial resolution, making it possible to determine the evolution of the spectral and spatial characteristics of the observed MHD instabilities. These analyzes revealed that during the initial stage of the plasma formation (when the plasma current is still increasing) magnetic islands with decreasing wave numbers, identified as edge kink modes, are detected in the Mirnov coils. After the plasma formation, when the equilibrium parameters are relatively flat (plateau), oscillations are detected in both Mirnov coils and SXR system, indicating the presence of MHD instability in the whole plasma column. In general, the fluctuations measured by the Mirnov coils have low amplitude corresponding to small magnetic islands, which were identified as tearing modes. On the other hand, the instabilities at the central region were identified as sawteeth oscillations that correspond to periodic relaxations in the internal region of the magnetic surface with safety factor q = 1 and that are accompanied by precursor oscillations which amplitude depends on the phase of the relaxation cycles. Due to this amplitude modulation, frequency satellite peaks appear in the spectrograms of the SXR signals. Furthermore, due to the fact that relaxation cycles are not sinusoidal, harmonics of the relaxation frequency also appear in the spectrograms. However, in many TCABR discharges, the intensity of the oscillations measured by the Mirnov coils increase significantly during the plateau, with affects the frequency of all MHD instabilities, even over the sawteeth in the central region of the column. In all cases, it was observed that during the plateau the frequency of the magnetic islands coincides with the frequency of the sawtooth precursors, although they are two different instabilities located in separated radial positions. This coincidence of frequencies allowed describing the frequency evolution of all measured oscillations by considering only two basic frequencies: the cycles of sawtooth relaxation and the magnetic islands.