One aspect as reported herein is using a method comprising the step of immunizing an experimental animal, three times with primary cynomolgus PBLs, whereby the PBLs are optionally enriched for T cells without using primary human PBLs as immunogen and without using a denaturing agent for producing a human cynomolgus cross-reactive antibody specifically binding to human CD3 epsilon of SEQ ID NO: 02 and specifically binding to a polypeptide of SEQ ID NO: 01, wherein the human cynomolgus cross-reactive antibody specifically binds to human and cynomolgus T cells, activates human T cells and does not bind to the same epitope as the antibody OKT3, the antibody UCHT1 and/or antibody the SP34.