Disclosed are a propylene 
polymer having a high 
crystallinity of a boiled 
heptane-insoluble component contained therein, a high stereoregularity and an extremely long mesochain (continuous propylene units wherein directions of alpha-methyl carbons are the same as each other), and a process for preparing said 
polymer. Also disclosed are a propylene block 
copolymer containing a crystalline 
polypropylene portion having a high 
crystallinity of a boiled 
heptane-insoluble component contained therein, a high stereoregularity and an extremely long mesochain, and a process for preparing said 
copolymer. Further disclosed is a propylene 
polymer composition comprising the above propylene polymer or propylene block 
copolymer and at least one stabilizer selected from a 
phenol type stabilizer, an organophosphite type stabilizer, a 
thioether type stabilizer, a hindered amine type stabilizer and a metallic salt of higher aliphatic acid. The propylene polymer of the invention is excellent in rigidity, 
heat resistance and 
moisture resistance, and can be favorably used for sheet, film, filament, injection molded product, blow molded product, etc. The propylene block polymer of the invention is well-balanced between rigidity, 
heat resistance and 
moisture resistance, and can be favorably used for sheet, filament, injection molded product, blow molded product, etc. The propylene 
polymer composition of the invention has excellent properties of the propylene polymer or the propylene block copolymer, and moreover is excellent in 
heat stability during the molding stage, long-term 
heat stability and 
weathering resistance. The propylene 
polymer composition can be favorably used for sheet, film, filament, injection molded product, blow molded product, etc.