Thermoplastic elastomer compositions can be use for medical applications, Comprising: a) 97.1 to 90.9 wt.-% star-shaped block copolymer A with identical arms of the structure [S1-(S/B)k-(S/B)I-(S/B)m-S2]n-X, where S1 and S2 are vinylaromatic hard polymer and S/B are soft random vinylaromatic/diene copolymer blocks; X is a coupling center; and b) 2.9 to 9.1 wt.-% plasticizer B.