Process for producing by blown film process a multilayer film containing at least one copolyamide layer and at least one polyolefin layer, in which the copolyamide comprises monomeric units of: •aliphatic non-cyclic diamines X and aliphatic non-cyclic dicarboxylic acids Y or aliphatic non-cyclic α,ω-amino acids Z, and •diamines M and diacids N in an amount between 0.1 to 2 wt % based on the total amount of copolyamide, and in which M and N are cyclic. The invention also relates to a multilayer blown film containing at least one copolyamide layer and at least one polyolefin layer, in which the copolyamide comprises monomeric units of: •aliphatic non-cyclic diamines X and aliphatic non-cyclic dicarboxylic acids Y or aliphatic non-cyclic α,ω-amino acids Z, and •diamines M and diacids N in an amount between 0.1 to 2 wt % based on the total amount of copolyamide, and in which M and N are cyclic.