A process for determining lateral overturning of a vehicle in which a threshold value line is established separating a lateral overturning region farther from an origin and a lateral non-overturning region closer to the origin on a two-dimensional map made using a rolling angle &thgr; and a rolling angular speed &ohgr; of the vehicle as parameters. When a hysteresis line for actual rolling angles and actual rolling angular speeds of the vehicle traverses the threshold value line from the lateral non-overturning region to the lateral overturning region, it is determined that there is a possibility of lateral overturning of the vehicle. When the rolling angular speed &ohgr; of the vehicle is increased sharply after the rolling angle &thgr; has reached a fully bumping rolling angle &thgr;FB while the rolling angular speed &ohgr; was decreased, it is determined that the vehicle is in a state in which the lateral overturning due to a rolling resonance phenomenon is liable to occur, whereby the threshold value line S is moved toward the origin.