Positron lifetime measurements are reported for linear poly(alpha -olefin)s from polypropylene to poly-l-eicosene polymerised using zirconocene catalyst. Fur comparison a low density polyethylene was also studied. Four lifetimes are resolved, the longest of them ( tau (4) is attributed to o-Ps annihilation from free-volume holes in the amorphous phase and is used to estimate the mean volume of these holes. It is observed that the hole size increases with increasing separation between the measuring temperature (T = 300 K) and the glass transition temperature T-g, estimated with differential scanning calorimetry. Among the poly(alpha -olefin)s the average hole volume is the largest in poly-l-dodecene (0.205 nm(3), T-g = 165 K) and the lowest in polypropylene (0.117 nm(3), T-g = 262 K). A method for estimation of the glass transition temperature T, from the experimental hold volumes is proposed. From comparison of amorphous and crystalline densities the fractional free volume was calculated. From this the number of holes was estimated to be 0.5-0.9 nm(-3). The effect of;exposure of the polymers to positron radiation from the source on the o-Ps annihilation parameters was also studied. While lower poly(alpha -olefin)s show a more or less pronounced exponential decrease of the o-Ps intensity I-4 as a function of time, a slight increase is observed in higher poly(alpha -olefin)s. Possible reasons for this behaviour are discussed. (C) 2001 Published by Elsevier Science Ltd.