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) 40 to 240 parts by weight of a non-aromatic
softening agent for rubber, (c) 5 to 300 parts by weight of
polyethylene or a copolymer composed mainly of
ethylene, and (d) 5 to 60 parts by weight of
polypropylene or a copolymer composed mainly of propylene, characterized in that the process comprises the following steps: (I) melt kneading the whole amounts of components (a), (b) and (d) and a part of component (c), and, at the same time or subsequently, melt kneading these with (f) an
organic peroxide, and (II) melt kneading the product obtained from step (I) with the remaining part of component (c), and component (c) is one which has been prepared using a
single site catalyst. The obtained composition is soft and excellent in heat deformation resistance and
mechanical strength, moldability and processability. The present invention also provide a
thermoplastic elastomeric resin composition comprising the above components (a), (c) and (d) in an amount of 100 parts by weight, 5 to 150 parts by weight and 5 to 80 parts by weight, respectively. The composition is soft and excellent in heat deformation resistance and
mechanical strength, moldability and processability and shows good results in the extraction tests.