The invention provides a process for the preparation of a
thermoplastic elastomeric resin composition comprising melt kneading (a) 100 parts by weight of a block
copolymer consisting of at least two polymeric blocks (A) composed mainly of a vinyl aromatic compound and at least one polymeric block (B) composed mainly of a
conjugated diene compound, and / or a hydrogenated block
copolymer obtained by hydrogenating said block
copolymer, (b) 20 to 300 parts by weight of a non-aromatic
softening agent for rubber, (c) 1 to 150 parts by weight of a
peroxide-crosslinking type olefinic resin and / or a copolymeric rubber containing said resin, and (d) 10 to 150 parts by weight of a
peroxide-decomposing type olefinic resin and / or a copolymer containing said resin, characterized in that the process comprises a step of heat-
processing component (a), component (b), at least a part of component (c), at least a part of component (d) and at least a part of 1.0 to 1,200 parts by weight of component (e) in the presence of an
organic peroxide to cause crosslinking, wherein component (e) is at least one
thermoplastic polymer selected from the group consisting of
polyester type (co)polymers,
polyamide type (co)polymers and
polyurethane type (co)polymers, and a subsequent step of blending these with the remaining part of component (c), and, the remaining part of component (d) and component (e), if any. The obtained composition is soft and excellent in heat deformation resistance and
mechanical strength, moldability and processability, particularly in oil resistance and
stain resistance.