Excitation of snake perturbations has been observed in the core region of pellet-fuelled HL-1M plasmas when the pellets cross the surface with a q value of 1. It is observed that the snake oscillations have an m = 1, n = 1 helicity with quite a long lifetime. A detailed comparison has been made between the locations of the q = 1 surface and the snake oscillation. Through measurements of the plasma q-profile by means of multi-exposures with a CCD camera during pellet ablation, and investigation of the pellet ablation process, possible mechanisms for the formation of the snake oscillation are discussed. In addition, a large, long-lived snake-like oscillation is frequently observed in lower-hybrid current driven (LHCD) discharge in which the sawtooth has been stabilized early in the discharge. There is evidence that such a perturbation is due to impurity accumulation during sawtooth-stabilization, and good performance with peaking profiles after LHCD is limited by magnetohydrodynamic instabilities including sawtooth and snake activities in HL-1M plasmas.