this thesis investigates mainly the molecular and intramolecular relaxation processes of some aromatic and aliphatic molecules containing rotatable polar groups and some analogous rigid molecules dispersed in (a) atactic polystyrene matrices and (b) cis-decalin. sample preparations and the dielectric measurements using general radio 1615a and 1621 capacitance bridges with appropriate temperature controllable cells have been described. the glass transition temperature (t[subscript g] ) measurements using the glass transition apparatus have also been described. the experimental data as a function of frequency at different temperatures were subject to analysis by a series of computer programs written in apl language. the activation energy barriers opposing the dielectric relaxation processes were obtained by the application of the eyring rate equation. of the spherically shaped rigid polar molecules examined in cis-decalin, both [beta]- and [alpha]-relaxations are detected in most of the compounds. dielectric data for [alpha]-relaxations are described by the cole-davidson skewed arc function. the ah values of the [beta]-process increase appropriately with molecular size but are largely independent of the glassy medium. the [beta]-processes for these systems are attributed to molecular relaxation which may possibly occur in a "solvent cavity". of the aromatic flexible molecules, a variety of anisoles have been studied in cis-decalin. in the systems studied methoxy group relaxation except for the para-fluoroanisole. the barrier to methoxy group rotation is independent of para-substitution and the choice of solvent...