The flashover failure and damage of polypropylene (PP) and polyester (PET) films under nanosecond current pulses were experimentally investigated. A nanosecond pulse current test platform was established to study the flashover characteristics, performance degradation, and structural damage of dielectric films under repeated nanosecond current pulses. The accumulation and emission of surface charge influenced by field distortion and trap distribution were analyzed to clarify the mechanism by which the flashover voltage increases linearly with gas pressure at low pressure and saturates at high pressure. The significant effects of pulse energy, gas pressure, and discharge gap on film damage behavior were investigated. The damage pattern of PP and PET films includes surface deformation, reduced flash-voltage tolerance, molecular chain breakage, and group shedding. The damage of PP films is manifested as fine furrows, while PET corresponds to mountainous bumps. With the increasing number of discharges, the breakdown voltage of PP films decreased significantly, while the flash tolerance performance of PET films was more stable. Under the conditions of high pulse current amplitude, small discharge gap, and low air pressure, the damage degree of the film intensifies, which is characterized by severe destruction to the molecular structure and a significant decrease in flashover withstand voltage. Polymer films, flashover, nanosecond current pulses; performance degradation; microstructural damage.