Using dielectric spectroscopy, some organic liquids consisting of mainly alkylhalides and acetic acid esters, have been studied over a wide frequency (10(6) to 10(-3) Hz) and temperatures (down to 77 K). Measurements have also been made in the true liquid state at four microwave frequencies of 33, 22.4, 10, and 5.4 GHz in the temperature range 303-363 K. The high-temperature data reveals a significant contribution from the intramolecular (end- or side-group) rotation. The data corresponding to the supercooled state reveals a secondary (beta) process in addition to the primary (alpha) process. The magnitude of the beta process is found to be relatively large in systems which have greater contribution from the intramolecular process to the overall polarization at room temperature. The activation energies together with the side/end-group dependence of the magnitude of the beta process suggest that the intramolecular process, though very much hindered during the process of supercooling, may survive to some extent in the glassy state to be realized as the beta-process. Our study suggests that the origin of the beta process in these glasses may not be intermolecular in nature.