Thermoplastic elastomer compositions can be used for medical skin contact applications, comprising: a) 90.9 to 69.0 wt.-% star-shaped block copolymer A with 4 arms of the general structure [S1—(S/B)k—(S/B)l—(S/B)m—S2]n—X, where S1 and S2 are vinylaro-matic hard polymer and S/B are soft random vinylaromatic/diene copolymer blocks; X is a coupling center; and b) 9.1 to 31.0 wt.-% of a plasticizer B: b 1) a mixture of mineral oil B1 and cyclohexane 1,2-dicarboxylic acid C8 to C10 dialkyl ester B2; or b2) a mixture of mineral oil B1 and vegetable oil B3.