Semicrystalline ethylene/1-octene copolymers (P(E-co-O)) with a content of 1-octene comonomer, w(O), between 7 and 24 wt% and a crystallinity X-c between 50 and 10% and a high-density polyethylene (HDPE, X-c = 70%) were studied in the temperature range between 115 K and (300-350) K by positron annihilation lifetime spectroscopy (PALS) and dynamic mechanical analysis (DMA). The samples were characterised by differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS). The T(g)s estimated from the thermal expansion of the local free volume estimated from the PALS data decrease linearly with w(O) between 251 K (extrapolated to w(O) = 0) and 220 K (w(O) = 24 wt%). They agree very well with those estimated from DMA (loss modulus E") and DSC. However, the T(g)s obtained from the maximum of tan 8 do not agree with all of the others, inparticular for higher crystallinities. For HDPE, any indication of glass transition could not be observed. From this it was concluded that the whole amorphous phase in this highly crystalline polymer is immobile. From the variation of the thermal expansivity of the local free volume the fractions of the mobile and immobile amorphous phase are estimated. It was observed that the o-Ps intensity shows a minimum at T-min approximate to T-g + 10 K.