The invention relates to a method for producing a multilayered part which comprises a moulded core (5) and a flexible polyurethane skin layer (4). The core itself comprises a moulded substrate layer (1) which is made of a substrate material, in particular a thermoplastic material, having a Shore A hardness higher than 60. The flexible polyurethane skin (4) is produced by a reaction overmoulding (ROM) process wherein a polyurethane reaction mixture is moulded in a closed mould (11, 12) over at least a first area of the core surface. The moulded core (5) comprises in addition to said substrate layer (1) a softer material which is moulded onto the substrate layer (1) and/or onto which the substrate layer (1) is moulded. This moulded softer material has a Shore A hardness lower than 60 and forms a softer layer (2) between the flexible polyurethane layer (4) and the substrate layer (1) and/or a seal (3) engaging the internal wall of the mould (11, 12) during the ROM process.