a general correlation function is firstly reviewed in line with kubo's formulation (chap. 1, (a)), and dielectric relaxation processes together with some fundamental properties are considered with the help of the function (chap. 1, (b)). the introduction of hoffmann's site model enables us to calculate a dielectric correlation function. this technique is applied to the dielectric relaxation of some molecules, (chap. 1 (c)). discussion with respect to the calculation of the molecular dipole moment for a molecule which contains two equivalent rotational groups is made (chap. 2, (a)). the results are applied to two convenient models, i.e., a free rotation model and a model called "free oscillation" which is proposed in this thesis. the latter model is employed for the cases of o-haloanisole and o-halothioanisole, experimental dielectric constant and loss data were analyzed by the cole-cole equation as well as budo's equation (chap. 3). rotation of the methoxy group in dimethoxy compounds was examined by relaxation time and dipole moment. the mean relaxation time for o-dimethoxybenzene is found to be short. (chap. 4). the variation of the relaxation time of the methoxy group of anisole is considered theoretically (chap. 4, (c)). mesomeric and double internal rotation mechanisms concerning the anomalously short relaxation time of diphenyl ether are discussed. correlation function treatments are made based on the former mechanism.( chap. 5). rotation around s-s bonds is concluded to be restrictive. (chap. 6). relaxation time and dipole moment values of difuryl mercury are explained in terms of the non-linearity of c-hg-c bond. (chap. 7).