The itinerant oscillator model whereby a typical molecule of a polar fluid map exhibit librational motion under the influence of the held of its large cage of neighboring dipoles is examined when the restriction of rotation about a common fixed axis is removed, both cage and tagged molecule now being free to rotate about a common fixed point of themselves. It is shown that the equations of motion of the system cannot, in general, be decomposed into the equations of motion of the tagged molecule relative to the cage and that of the cage alone on account of the Coriolis torques. If, however, one can make the assumption that the cage is much more massive than the tagged molecule so that in a short time (essentially a time less than the Debye relaxation time of the cage so that the cage represents a slowly relaxing local structure) after the removal of an external uniform field the cage remains virtually at rest relative to the tagged molecule, then the dipole autocorrelation function of the tagged molecule is approximately the product of the autocorrelation function of the cage and the autocorrelation functions of the motion of the ta Fed molecule relative to the cage. The behavior of the model, with a cage-dipole interaction potential including both the permanent and induced dipole terms in the noninertial limit is discussed using the above assumption. It is shown that the inclusion of the induced dipole term essentially creates an asymmetric bistable interaction potential in which a relaxation process indicative of a slow overbarrier (activation) process coexists with the relatively fast relaxation modes in the wells of the potentials [as predicted by Polemino and Freed, Adv. Chem. Phys. 83, 89 (1993) in their numerical analysis of the model]. The conditions under which the fast relaxation processes may come to dominate the overall relaxation behavior are discussed by analogy with superparamagnetic relaxation [cf. Coffey, Crothers, and Kalmykov, Phys. Rev. E 55, 4812 (1997)]. (C) 1997 American Institute of Physics.