Chitosan is a natural polymer well known for its efficient uptake of heavy metals. The modification of this polymer by the substitution of functional groups from organic acids allows new sorbents with high sorption capacities to be obtained: NDTC with ascorbic acid and glutamate glucan with oxo-2-glutaric acid. The mechanism of sorption is investigated and several sorption models are applied such as the Freundlich, Langmuir and Temkin models which fit experimental results well. These results are explained by the heterogeneity of the polymer surface, the variability of metal species in solution and possible interactions between the molecules sorbed. The effects of several parameters such as pH and metal ion concentration are examined and demonstrate the relative importance of metal speciation on sorption performances and mechanisms. The grafting of functional groups creates some heterogeneity of sorption energy, which explains the selectivity seen in the best models. Metal ions are firstly bound onto more energetic sites (nitrogen groups) and later onto other substituting functions.