The invention relates to novel adhesive alpha-olefin inter-polymers which are largely amorphous and have a rheological behavior that makes them suitable for adhesive use, both without and with minimzed amounts of tackifying resins. Specifically, the invention poly-alpha olefin inter-polymer may be composed of A) from 60 to 94% of units derived from one alpha mono-olefin having from 3 to 6 carbon atoms and B) from 6 to 40 mol % of units derived from one or more other mono-olefins having from 4 to 10 carbon atoms and at least one carbon atom more than A); and C) optionally from 0 to 10 mol % of units derived from another copolymerizable unsaturated hydrocarbon, different from A) and B); the diad distribution of component A in the polymer as determined by .sup.13C NMR as described herein showing a ratio of experimentally determined diad distribution over the calculated Bernoullian diad distribution of less than 1.07; and the storage modulus G' of said polymer, determined upon cooling as described herein, intersecting a value of 3.10.sup.5 Pa at a temperature of less than 85.degree. C. The invention also describes polymerization processes suitable for the manufacture of these adhesive alpha-olefin inter-polymers.