Poly(4-methyl-1-pentene) (PMP) is using up to now as the hollow fiber air separation membranes. This polymer with good resistance to organics attack can be prospective for separation of lower hydrocarbons.An attempt for the theoretical consideration and experimental study of the C1-C3 alkanes diffusion in poly(4-methyl-1pentene) (PMP) as a binary system in the temperature range from 253,K to 353, K covering the glass transition region of PMP (~ 303, K) is carried out in this work. The permeability of CH4, C2H6, C3H8 has been measured by the permeability differential method under the partial pressure drop across the membrane 1 bar with the gas chromatography analysis of the permeate flux. The diffusion coefficients have been calculated from the experimental differential permeability curves by using linearization method developed earlier. Novelty of results is that at temperatures below Tg PMP can be considered as a single-phase system from the gas transfer point of view. At the temperatures above Tg PMP can be considered as a two-phase medium with diffusion coefficients of C1-C3 alkanes in amorphous (Da) and crystalline phases (Dc) (Da>Dc) which differ by not more than an one order of magnitude. For the first time it is shown that the diffusivity of C1-C3 alkanes in amorphous and crystalline PMP phases is decreasing in accordance with sequence DCH4 >DC2H6 >DC3H8. A certain scatter of the PMP data published in the literature was noted. Obtained data can be relatively compared with published ones only for methane: for virgin PMP films we obtained PCH4 = 16.7 Barrer; it is known for the extrusion PMP films that PCH4 = 14.6 -19.8 Barrer, for casted PMP films PCH4 = 0.4 -1.2 Barrer. The values for ethane and propane in crystalline phase of PMP are obtained for the first time. Evaluation of permeability through crystalline phase at temperature 313,K shows that PC2H6 = 15 Barrer; PC3H8 = 5 Barrer. For real estimation of the separation efficiency PMP it is needed an additional research with taking into account the crystallinity and temperature dependences for diffusivity based on results of this study.