The major problems existing in the derailment studies are summarized according to analysis of the research status about train derailment in China and other countries of the world.(1) The current criteria for preventing derailment cannot assure that derailment will not occur.(2) It is not clear for train derailment mechanism.(3) There exist three fundamental problems in the calculation of train derailment as follows: ① The connecting condition of displacement between wheel and rail cannot be satisfied in establishment and solution of vibration equation group of train-track(bridge) time-variant system.② Only the lateral track irregularity is regarded as the exciting source of lateral vibration of train-track(bridge) time-variant system.The true exciting source,i.e.the wheel and rail contact status is neglected.③ The random lateral vibration of train-track (bridge) time-variant system is analyzed according to the random track irregularity and analysis theory of random vibration of time-invariant system.But the maximum responses of lateral vibration of train-track(bridge) time-variant system cannot be calculated,and furthermore train deraiment cannot be forecasted.The thinking and methods for solving these problems are also introduced.The train derailment mechanism,which is the result of losing stability in lateral vibration status of train-track(bridge) time-variant system,is proposed for the first time by analysis of characteristics of self-excitation of train vibration and losing stability in self-excitation vibration status of train derailment.So the key to analyzing train derailment is to analyze the stability of lateral vibration of train-track(bridge) time-variant system.The following conclusions are made by summarizing the existing analysis theory of stability of static and dynamic system.(1) Because of the characteristics of time-variant and self-excitation of train-track(bridge) system,the stability of lateral vibration of the system cannot directly be analyzed by the existing analysis theory of stabi
