We discuss the features of cross-polarization (CP) between dilute spin systems with substantial molecular motion and discuss the applicability of two different theories for the description of cross-polarization in toluene-solvated fullerene-70. The material was examined by C-13 --> H-1 and H-1 --> C-13 CP NMR with magic-angle spinning (MAS). C-13 --> H-1 CP was set on perdeuterated glycine. Both solids were at the natural C-13 isotopic abundance and with ca. 2% H-1 content, so that C-13 and H-1 spin species were both dilute. We have found that CP between the fullerene carbons and the toluene protons in either direction is not site-specific and its kinetics are governed by the same time constants. This result and the measured signal intensities are rationalized in terms of the short-correlation-time theory of CP. The toluene carbons cross-polarize only from the adjacent protons according to the classic CP theory. There are two kinds of toluene molecules with the relaxation time T-1 rho(H) of 10 and 70 ms. The former molecules are single and more mobile, and the latter, less mobile, probably form aggregates. CP between the dilute spin systems is very sensitive to molecular motion.