596712 Disclosed is an isolated anti-CXCR4 antibody, or one of its functional fragments, wherein said antibody comprises: a light chain comprising CDR-L1, CDR-L2 and CDR-L3 comprising respectively the 5 amino acid sequence SEQ ID Nos. 1 (QSLFNSRTRKNY), 2 (WAS) and 3 (MQSFNLRT); and a heavy chain comprising CDR-H1, CDR-H2 and CDR-H3 comprising respectively the amino acid sequence SEQ ID Nos. 4 (GFTFTDNY), 5 (IRNKANGYTT) and 6 (ARDVGSNYFDY); or a light chain comprising CDR-L1, CDR-L2 and CDR-L3 comprising respectively the amino acid sequence SEQ ID Nos. 1 (QSLFNSRTRKNY), 2 (WAS) and 30 (KQSYNLRT); and a heavy chain comprising CDR-H1, CDR-H2 and CDR-H3 comprising respectively the amino acid sequence SEQ ID Nos. 31 (GFSLTDYG), 32 (IWGDGTT) and 33 (ARGRQFGFDY).