Literature data of NMR 1H and 13C spectra of linear alkanes X-(CH2)(n)-Y (I), (where X = H; Y - 38 different substituents, including H and CH3) were considered. The new universal way of estimating the chemical shifts values of the methylene groups (delta(H) CH2 - - delta(H) (i), delta(C) (CH2) - delta(C) (i), i = 1-38) in I was proposed. The concept of it considers changes in the values delta(H) (i) and delta(C) (i) of each methylene groups in I (called as increments Delta delta(H) (i) and Delta delta(C)(i)) as a result of conversion to I of a hypothetic alalkane -(CH2)(k)-(CH2)(n)-(CH2)(l)- (II) by replacing infinitely long fragments -(CH2)(k)-and -(CH2)(l)-of it with the substituents X and Y. Increments Delta delta(H) (i) and Delta delta(C)(i) for all substituent types were calculated and tabulated. The proposed method allows to calculate the delta(H) (i) and delta(C) (i) parameters for the unpublished NMR H-1 and C-13 spectra of long- and medium-chain compounds I. The example of calculations was given.