Block copolyetheramides, well adopted for conversion into a wide variety of useful thermoplastic elastomer shaped articles, have the formula: ##STR1## in which D is the residue of a diacid oligamide having an Mn ranging from 300 to 3,000 and/or the residue of the diacid chain limiter, PE is the residue of a polyetherdiol having an Mn ranging from 200 to 5,000,.times.is a straight or branched chain (cyclo)aliphatic or aromatic hydrocarbon having from 4 to 20 carbon atoms, n is a number ranging from 1 to 4, and m is an average number ranging from 2 to 50; these are prepared by polycondensing a multiblock polymer having the formula: ##STR2## with a diamine H.sub.2 N--X--NH.sub.2.