Production method of a transgenic mouse expressing human Ig-κ light chains and human Ig-λ light chains, comprising the steps of: (A) producing a mouse embryonic stem cell (ES) comprising a λ light chain locus human, in the germline configuration, and stably integrated into the genome of the ES cell, in which said λ light chain locus comprises the Vλ gene segments from 5 'of the Vκ gene 1-27 to 3 'of the enhancer of λ in 3'； (B) produce a transgenic mouse from the ES cell of step (A)； and (C) matching said transgenic mouse of step (B) with a transgenic mouse whose genome comprises: (i) a stably integrated part of a human κ light chain locus in the germline configuration, wherein said part comprises the genes of Vκ beginning in Vκ-B3 and ending in Vκ-OP11, with a deletion of Vκ-LP13 to Vκ-LP6； the Jκ region； the Cκ region； the element of deletion of κ； and the 3 'and intronic enhancers of lgκ； and (ii) a stably integrated part of a human immunoglobulin heavy chain locus in the germline configuration, wherein said part comprises the VH genes starting at VH6-1 and ending at VH3-65: the region DH, the JH region, the genes of the Cμ constant region, the genes of the Cδ constant region, the genes of the Cγ constant region, the 3 'mouse enhancer and the human intronic enhancer, in which said genes of the Cγ constant region are selected from the group consisting of: genes from the human Cγ1 constant region, genes from the human Cγ2 constant region and genes from the human Cγ4 constant region； (iii) homozygous inactivated endogenous immunoglobulin heavy chain loci； and (iv) homozygous inactivated endogenous immunoglobulin κ light chain loci； to produce a transgenic mouse as offspring whose genome comprises: (a) said human λ light chain locus, in the germline configuration, and stably integrated； (b) said stably integrated part of a human κ light chain locus in the germline configuration: (c) said stably integrated part of a human immunoglobulin heavy chain locus in the germli
