Polyolefinic compositions comprising: (A) 1-99% by weight of a propylene amorphous polymer, and (B) 1-99% by weight of a copolymer selected from (BI) a copolymer of propylene with ethylene and/or alpha-olefins C4-C10, and (BII) a composition comprising: (a) 10-50% by weight of an isotactic polypropylene with ethylene and/or alpha-olefins C4-C10; (b) 0-20% by weight of a copolymer containing ethylene, insoluble in xylene, and (c) 40-80% by weight of an elastomeric copolymer of ethylene with propylene and/or alpha-olefins C4-C10, optionally with small amounts of diene. These compositions are endowed with good mechanical and optical properties and are suitable for the manufacture of articles for biomedical applications.