V-t characteristics were measured and the thermal bubble deformation was observed in liquid nitrogen and helium with a ramped voltage, simulating the quenching conditions in large superconducting magnet coils. From the experimental results, the breakdown process of liquid coolants in the presence of thermal bubbles was classified into three categories depending on the voltage slope: (1) breakdown through a composite insulation system of undeformed bubbles and surrounding cryogenic liquid with fast rising voltage such as the standard lightning impulse voltage; (2) breakdown through a strongly elongated bubble by an electric field with the rise time of milliseconds; and (3) breakdown through a vapor bridge of the gap, formed by growth of a bubble fixed on an electrode with a hot spot, by electric fields rising in approximately 100 ms. >