The Berne-Pechukas-Kushick potential for linear molecules, together with a central electric point dipole, has been used as the model for polar liquids in a series of molecular dynamics computer simulations. Different simulations used Ewald summation, spherical cut off and spherical cut off with reaction field correction to sum the dipole-dipole interactions, and the relative merits of these methods are discussed. Results for thermodynamic properties and the distribution function
h
∆
(
r
) are presented. Results for the autocorrelation functions for dipole orientation and angular velocity are also presented, and discussed in terms of memory functions, particularly with regard to the Steele perturbation theory. The complex, frequency-dependent dielectric constant has been calculated from the memory function of the autocorrelation function of the periodic cube dipole moment, and results are presented in the form of Cole-Cole plots. The ‘dielectric friction’ approach to polar liquids is examined against the evidence of the molecular dynamics data. Attention is drawn to the behaviour of the cross correlations between dipole orientations and their importance to the problem of dielectric relaxation is emphasized.