Parameter estimation from experimental data is a crucial problem in quantitative modeling of biochemical reaction networks. An especially important issue, raised by the complexity of the models and the challenging nature of the experimental data, is parameter identifiability. Despite several approaches proposed in the systems biology literature, no agreement exists on the analysis of structural and practical identifiability, and the relations among the two. In this paper we propose a mathematical framework for the analysis of identifiability of metabolic network models, establish basic results and methods for the structural and practical identifiability analysis of the class of so-called linlog models, and discuss the results on the basis of an artificial example.