Linear long-chain organic molecules are known to form lamellar intermediate phases (called also rotator phases) between their fully ordered crystalline phases and their isotropic liquid phases. The temperature range of occurrence and the properties of these intermediate rotator phases are crucially important for the texture of many food and cosmetic products, for the flow of various phase-change materials used in energy storage and transport, and for several processes in living nature, such as the formation of superhydrophobic and self-healing cuticle layers in plants and insects. Nevertheless, data for the rheological properties of such peculiar materials below their melting point, Tm, are almost missing, due to the specific difficulties in the respective rheological measurements. In the current study we describe a methodology for measuring and comparing the shear rheological properties of rotator (R) and crystalline (C) phases formed in bulk hydrocarbons at temperatures below Tm. We apply this approach to characterize the rheological properties of R and C phases formed upon cooling of alkanes with chain length varied between 17 and 30 carbon atoms. For comparison, we study also several alkane mixtures and one alkene with double bond at the end of its chain. The obtained results show that the storage and loss moduli of the rotator phases are ca. 10-times lower than those of the respective crystalline phases. We found also that the rheological properties of the crystal phases depend mainly on the subcooling temperature below the crystallization temperature, TC, while the R phases become softer with the increase of the molecular length. We explain these results by assuming that the rheological properties of the crystal phases are determined mainly by the sliding of the ordered crystal domains with respect to each other, while in the rotator phases we have multiple defects in the molecular packing which increase with the alkane length. The proposed methodology and the obtained results serve as a solid basis for further rheological studies of this important class of technological systems.