Application of real-time Raman longitudinal acoustic mode (LAM) spectroscopy is demonstrated in the studies of comparatively fast crystallising and transforming monodisperse polyethylene oligomers. The experiments have confirmed the structural model of the transient non-integer folded (NIF) form in long-chain n-alkane C246H494 derived previously from real-time small-angle X-ray scattering (SAXS). During crystallisation of the NIF and its subsequent isothermal transformation into the once-folded form F2 a single fundamental (LAM-1) peak of constant frequency is observed, which corresponds to the straight chain segment length exactly equal to half the full chain length. This confirms that crystalline core layers of the NIF have a constant thickness corresponding to that of the once-folded form F2. The remaining thickness making up the full lamellar periodicity thus consists of an amorphous layer made up of cilia. The constant frequency, but increasing intensity of the LAM-1 band during isothermal annealing is consistent with the cilia crystallising by re-entering the existing crystalline layers. In alkanes C210H422 and C198H398 another mechanism of transformation of the NIF into a more stable structure is observed. A new mixed-integer folded-extended (FE) phase forms instead of the pure once-folded F2 phase. Instead of re-entering the existing crystal layer, the cilia from two neighbouring NIF lamellae gather and form a third intracalated crystalline layer. The resulting superstructure contains three crystalline layers in a repeat unit. Whether one or the other of the two, transformation modes take place appears to depend on factors such as fraction of folded chains in the NIF, overcrowding at the crystal-amorphous interface and chain diffusion.