The character of packing of double-stranded DNA molecules in particles of liquid-crystal dispersions formed as a result of the phase exclusion of DNA molecules from aqueous salt polyethylene glycol solutions has been estimated by comparing the circular dichroism (CD) spectra of these dispersions recorded at different osmotic pressures and temperatures. It is shown that the first cycle of heating of dispersion particles with hexagonally packed double-stranded DNA molecules leads to the occurrence of abnormal optical activity of these particles, which manifests itself in the form of a strong negative CD band, characteristic of DNA cholesterics. Moreover, subsequent cooling is accompanied by a further increase in the abnormal optical activity, which indicates the existence of the "hexagonal → cholesteric packing" phase transition, controlled by both the osmotic pressure of the solution and its temperature. The result obtained can be described in terms of "quasi-nematic" layers composed of orientationally ordered DNA molecules in the structure of dispersion particles. There are two possible ways of packing for these layers, which determine their hexagonal or cholesteric spatial structure. The second heating → cooling cycle confirms these results and is indicative of possible differences in the packing of double-stranded DNA molecules in the hexagonal phase, which depend on the osmotic pressure of the solution.