Iodine 129 is a radioactive waste produced by the nuclear industry. Due to its high volatility, it cannot be vitrified in conventional borosilicate glasses. This paper investigates the feasibility of iodine conditioning using a glass matrix intended for long-term storage in a geological repository. Silver phosphate glasses, which can incorporate high amounts of iodine and can be synthesized at low temperature, were chosen for this study. In order to increase their chemical durability, the glasses were cross-linked by niobium and bismuth oxides. Niobium and bismuth incorporation limits were determined for an iodine amount of 12 wt% and ranged from 1.6 mol% to 4.0 mol%, depending on the Ag2O/P2O5 ratio. The glass structures were investigated using 31P MAS NMR, RAMAN spectroscopy and X-ray absorption spectroscopy. The iodine local environment was determined by EXAFS at iodine K-edge. Structural investigations showed that the introduction of these crosslinking reagents induces a significant increase in the polymerization degree of the glasses. However despite this higher connectivity, the two crosslinking reagents have a low impact on the glass transition temperature after iodine addition.