Neutron diffraction (ND) analyses of ancient metals show that this method is capable of detecting differences in the inner composition and microstructure of ancient metal objects. Here, ND measurements were conducted on two 'eye shaped' axes from the end of the 3rd-beginning of the 2nd millennium BC. The objects were excavated from the ancient cemetery of 'Enot Shuni' Israel; one is made of bronze and the other of silver. Both artefacts are rare finds, with the silver axe unique in the archaeology of Israel, and therefore had to be analysed locally. For that purpose, a newly assembled diffractometer (KARL) at the IRR-1 of the Nuclear Research Centre (Soreq, Israel) was used. ND measurement on the bronze axe revealed the existence of an @a-phase with a range of Cu/Sn ratios (Cu-Sn solid solutions) and some amount of a @d-phase (intermetallic compound of Cu and Sn). The silver axe ND pattern shows the existence of an @a-phase (Ag-Cu solid solution) and some amount of copper metal. Our ND data are discussed in comparison with XRF surface measurements and thermal neutron radiography. The results are shedding more light on the in-depth material composition profile, as well as on the objects' structural and compositional affinities, and help to better understand the production processes and assist in conservation decisions.