In the self-guided molecular dynamics (SGMD) simulation method, a continuously updated average force is used to bias the motions of the system. The method appears to sample the configuration space of a number of complex systems more efficiently than ordinary molecular dynamics, and it was argued that it yields canonical averages of observable quantities with only negligible errors. We analyze the dynamic mapping associated with the SGMD algorithm and find that the dynamics lacks reversibility because the effective potential that governs the motion is a functional of the trajectory rather than a function of the coordinates (i.e., the dynamics is not uniquely specified by the initial conditions but depends on past history as well). This irreversibility is shown to result in substantial errors in canonical averages for model systems. Motivated by this analysis, we introduce an alternative self-guided scheme (the momentum-enhanced hybrid Monte Carlo method) that does converge to the canonical distribution in principle. The method differs from the original SGMD algorithm in that momenta, rather than forces, are averaged to bias the initial choice of momenta at each step in a hybrid Monte Carlo procedure. The relation of the method to other enhanced sampling algorithms is discussed. (C) 2003 American Institute of Physics.