Two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) studies on the rigid rodlike cholestane (CSL) spin-label in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments were performed over a wide temperature range : 96 degrees C to 25 degrees C covering the isotropic (I), nematic (N), smectic A (S-A) smectic B (S-B), and crystal (C) phases. It is shown that 2D-FT-ESR, especially in the form of 2D-ELDOR (two-dimensional electron-electron double resonance) provides greatly enhanced sensitivity to rotational dynamics than previous cw-ESR studies on this and related systems. This sensitivity is enhanced by obtaining a series of 2D-ELDOR spectra as a function of mixing time, T-m, yielding essentially a three-dimensional experiment. Advantage is taken of this sensitivity to study the applicability of the model of a slowly relaxing local structure (SRLS). In this model, a dynamic cage of solvent molecules, which relaxes on a slower time scale than the CSL solute, provides a local orienting potential in addition to that of the macroscopic aligning potential in the liquid crystalline phase. The theory of Polimeno and Freed for SRLS in the ESR slow motional regime is extended by utilizing the theory of Lee et al. to include 2D-FT-ESR experiments, and it serves as the basis for the analysis of the 2D-ELDOR experiments. It is shown that the SRLS model leads to significantly improved non-linear least squares fits to experiment over those obtained with the standard model of Brownian reorientation in a macroscopic aligning potential. This is most evident for the S-A phase, and the use of the SRLS model also removes the necessity of fitting with the unreasonably large CSL rotational asymmetries in the smectic phases that are required in both the cw-ESR and 2D-ELDOR fits with the standard model. The cage potential is found to vary from about k(B)T in the isotropic phase to greater than 2k(B)T in the N and S-A phases, with an abrupt drop to about 0.2k(B)T in the S-B and C phases. Concomitant with this drop at the S-A-S-B transition is an almost comparable increase in the orienting potential associated with the macroscopic alignment. This is consistent with a freezing in of the smectic structure at this transition. The cage relaxation rate given by R(c), its "rotational diffusion coefficient," is of order of 10(7) s-(1) in the I and N phases. It drops somewhat in the S-A phase, but there is a greater than order of magnitude drop in R(c) for the S-B and C phases to about 10(5) s(-1). This drop is also consistent with the freezing in of the smectic structure. The rotational diffusion tensor of the CSL probe is significantly larger than R(c) which is consistent with the basic physical premise of the SRLS model. In particular, R(perpendicular to)(0) and R(parallel to)(0) are of order 10(8) s(-1) and 10(9) s(-1) respectively.