A branched alpha-olefinic polymer composition having excellent melt flowability, good moldability and excellent melt tension and comprising at least two branched alpha-olefinic polymers each composed of (A) recurring units derived from a branched alpha-olefin containing 5 to 10 carbon atoms and having a branch at the 3-position or a position of a higher number and (B) recurring units derived from a linear alpha-olefin containing 2 to 20 carbon atoms; and a process for producing this polymer composition by a multiplicity of polymerization steps using a catalyst formed from (A) a highly stereoregular titanium catalyst component comprising magnesium, titanium, halogen and an electron donor as essential ingredient, (B) an organoaluminum compound and (C) an electron donor.