Three proposals for the propagation of the quantum time-dependent self-consistent field equations are presented. One is obtained by combining Zhu and Zhao's time-independent-like split-operator method [W.S. Zhu, X.S. Zhao, J. Chem. Phys. 105 (1996) 9536] and a predictor-corrector technique. By defining a time-independent quasi-Hamiltonian operator for the total system, two new split-operator propagators are proposed. Comparisons with the simple split-operator and second-order difference methods in a two-dimensional model system, the Henon-Helies potential, show that the three new methods all have better accuracy and higher stability.