We derived an expression that enables the accurate estn. of equil. properties using non-Hamiltonian dynamics. The major advantage of our scheme is that a time av. over a single non-Hamiltonian trajectory can be employed instead of an ensemble av. Hence, it can directly be used in std. mol. dynamics simulations. The connection between non-Hamiltonian dynamics and equil. properties was established by assigning to the individual frames of the trajectory a wt. that was based on the fluctuations of the phase space compression factor. Addnl., a simple scheme that takes into account only fluctuation of a given max. duration was introduced to reduce the statistical error. By systematically extending the duration of the allowed fluctuations, increasingly accurate results can be obtained. Non-Hamiltonian dynamics schemes that are capable to enhance sampling efficiency are applied to two model systems in order to demonstrate the practical performance of our approach for the calcn. of equil. free energy differences and probability d. profiles. [on SciFinder (R)]