A propylene/ethylene/&agr;-olefin terpolymer characterized in that i) there is from 0.01 mol % to less than 15 mol % of a comonomer unit with a molar ratio of ethylene units/C4-C20 &agr;-olefin units being in the range of from 6.5×10−4 to 0.99, and from more than 85 mol % to not more than 99.99 mol % of a propylene unit with 2,1- and 1,3-propylene units being in the range of from 0 to 1 mol %, in a polymer chain determined by 13C-NMR spectroscopy; ii) a weight average molecular weight (Mw) determined by GPC is in the range of from 40,000 to 1,000,000; and iii) the amount of the component eluted in o-dichlorobenzene at a temperature of not higher than 40° C. is not more than 10 % by weight based on the total weight of the terpolymer and the amount of the component eluted in o-dichlorobenzene within the ±10° C. range of an elution peak temperature is not less than 75 % by weight based on the weight of the component eluted at a temperature of higher than 0° C.