The wheel flange climb derailment and wheel impact derailment are studied. Firstly, it is assumed that the wheel flange climb process is quasi-static, then the flange climb derailment criteria are derived through analyzing the forces exerted on the wheelset. One criterion is the classical derailment formula that assumes friction sliding between wheel and rail occurs. Another is the so-called approximate analytical formula that considers the effect of wheel/rail creep forces. The calculations of an example indicate that the results of the classical method are more conservative compared with the results of the analytic method for the diagnosis of wheelset derailment. The laboratory test for the flange climb derailment with a single wheelset test stand is also undertaken to validate the theoretical analysis. Secondly, the wheel impact derailment, a kind of dynamic derailment, is investigated. The analytic solutions for the tangential motion of the wheel/rail contact point and the jumping height of the wheel are derived. The derailment criteria by using the wheel jumping height and the lateral impact force to wheel vertical load ratio are given. The influences of wheelset lateral impact velocity, flange angle, wheel/rail friction coefficient, wheel vertical load and impact time interval on wheelset derailment are analyzed.