Energetically preferable orientational states for linear nonpolar molecules are determined which result from the competition of quadrupole-quadrupole and Van der Waals dipole-dipole interactions. It is shown that with the decreasing intermolecular distance a and hence with the increasing Van der Waals contribution to the total energy, the system concerned successively passes through the following orientational phases: alternating longitudinal and transverse molecular orientations relative to the chain axis (phase I), planar arrangement of molecules inclined to the chain axis at some angle which tends to diminish with decrease in a (phase II), molecules aligned parallel to the chain axis (phase III). In contrast to the continuous transition between phases II and III, the nature of the transition I --> II depends on the radius of the interactions taken into account. In the approximation of short-range interactions, the phase transition represents a jump, whereas long-range interactions, if included, lead the system to change continuously from inhomogeneous to homogeneous structure in a narrow range of intermolecular distances. The applicability of the results obtained in the description of orientational structures of adsorbed nonpolar molecules is discussed.