The invention relates to hyperbranched copolyamides (HBPAs), to their production and to their use as additives, in particular as melt viscosity modifiers in thermoplastic polymer compositions.This copolyamide is obtained by a reaction between a monomer (I): A—R—Bf with A and B=polymerization functions of a 1st and 2nd type, respectively, which are capable of reacting with each other, R=hydrocarbon-based species and f=total number of B per monomer (preferably 2≦f≦10); and a monomer (II) A′—R′—B′ or the corresponding lactams, with A′, B′ and R′ having the same definition as that given above for A, B and R, respectively. This HBPA has a I/II molar ratio such that 0.125≦I/II≦2. One of the species R or R′ of (I) or (II) is aliphatic, cycloaliphatic or arylaliphatic.For example: A=NH2 and B=COOH or A=COOH and B=NH2 with F=2.A′=NH2 and B′=COOH or A′=COOH and B′=NH2.A—R—B2, e.g.: 5-aminoisophthalic acid or 3,5-diaminobenzoic acid and A′—R′—B′=ε-caprolactam.The yarns, fibres, films and moulded parts obtained using polymer compositions (e.g. PA) to which are added HBPA according to the invention are also included in this invention.