We present efficient adaptive numerical solution methods for systems of nonlinear Schrödinger equations associated with the multiconfiguration time-dependent Hartree-Fock method for the solution of the multi-electron time-dependent Schrödinger equation. The methods in our focus comprise splitting methods, exponential integrators and Lawson methods. We demonstrate that in the light of the high computational effort for the evaluation of the nonlocal operator associated with the potential part, Adams-Lawson multistep methods with a predictor/corrector step provide an optimal work/precision relation and also stable long-term integration. The corrector also provides an error estimator without additional computational effort, and thus adaptive time-stepping can be realized. This is demonstrated to reflect well the smoothness of the solution. Furthermore, the convergence of Adams-Lawson multistep methods for the MCTDHF equations is proven theoretically under minimal assumptions on the regularity of the exact solution.