A thermoplastic elastomer (TPE) for overmolding (OM) a nylon substrate with an overmolded layer consists essentially of an inert filler, a plasticizer, preferably a mineral oil, and chosen combinations of ingredients from the following: (i) a functionalized "high rubber" SHDS (styrene-hydrogenated diene-styrene) having a functionality of 1%, the "small end blocks" together present in an amount in the range from about 8-25% by weight; (ii) hydrogenated SDS or SHDS block copolymer having polystyrene endblocks and a polymerized vinyl aromatic monomer in the poly(conjugated diene) midblock, the polystyrene endblocks together present in an amount in the range from 20-30% by weight of the block copolymer, excluding weight of the polystyrene in the polydiene midblock; (iii) a functionalized "high rubber" SHDS having a functionality of >1% but <2%, the "small end blocks" together present in an amount in the range from about 8-25% by weight; (iv) from 0-30% by weight of the composition, of a functionalized polyolefin (F3), the olefin having from 2 to 4 carbon atoms; (v) from 0-15% by wt of the composition, of a hydrogenated nonfunctionalized hydrogenated polystyrene-poly(conjugated diene)-polystyrene (SHDS) block coplymer; and, (vi) an additive to enhance the useful life of the composition.