Process for continuously producing propylene-based block copolymer

A process for continuously producing a propylene-based block copolymer, which process comprises:

• a first polymerization step comprising polymerizing .alpha.-olefin comprising propylene in the presence of hydrogen and a stereoregular polymerization catalyst comprising a solid catalyst component containing magnesium, titanium, a halogen atom and an electron-donor compound, an organoaluminum compound and, if required, an electron-donor compound in a single polymerization reactor;
• a step of separating the polymer existing in the first polymerization step into a polymer (1) having an average catalytic efficiency, CE, which is not less than 1.1 times that of the polymer existing in the first polymerization step, and a polymer (2) having an average catalytic efficiency, CE, which is less than 1.1 times that of the polymer existing in the first polymerization step, said polymer (1) being supplied to a second polymerization step;
• a second polymerization step comprising transporting .alpha.-olefin polymer obtained in the first polymerization step to a copolymerization reactor and copolymerizing propylene with an .alpha.-olefin other than propylene in a gas phase substantially in the presence of said stereoregular polymerization catalyst used in the first polymerization step;
• an index n which represents the sharpness of a particle size distribution of said solid catalyst component being not less than 5 when a particle size distribution thereof is approximated to the Rosin-Rammler distribution;
• and
• an average catalytic efficiency, CE, of polymer discharged from the first polymerization step and supplied to the second polymerization step being not less than 1.1 times an average catalytic efficiency, CE, of the polymer existing in the first polymerization step.