A propylene polymer can be produced which has evenness of composition and regulated stereoregularity and is highly flowable and highly flexible. Also provided is a propylene-based modifier giving a molding which is soft, reduced in tackiness, and excellent in compatibility with polyolefin resins. Furthermore provided is a hot-melt adhesive composition. It is excellent in heat resistance and flowability at high temperatures and in adhesion to lowly polar substances. It is usable for sanitary materials, packaging, bookbinding, fibers, woodworking, electric materials, canmaking, building, bagmaking, etc.