The applicability of time-reversible integrators to the recently developed quantal cumulant dynamics (QCD) is examined, and their accuracy and efficiency are demonstrated by comparison with the Runge-Kutta method. We proposed three schemes, which differ in their partitions and orders of an exponential function of a Liouvillian. Three-part partition conserves the total energy with sufficient accuracy, whereas the two-part one does not. It is found that the equations of motion of the QCD are sensitive to the order. The sensitivity is due to the accordance of fractional time in variables, which contribute to the total energy, after the propagation. (c) 2007 Elsevier B.V. All rights reserved.