A molecular-dynamical formulation of the Hartree-Fock (HF) method is presented. The simulated-annealing and simulated-quenching (steepest-descent) techniques are applied to the minimization of the HF energy functional and to the solution of the HF equations. In a test application to the helium atom with Gaussian basis sets both techniques show good performances but have two drawbacks: an excessive number of Fock-matrix calculations and a slowing-down behaviour close to convergence. We propose a new multistep algorithm for the simulated-quenching technique in which both drawbacks are removed: the Fock-matrix calculations are reduced to a minimum and the slowing down does not occur. The resulting program is several times faster than standard self-consistent-field HF programs.