The study of gene regulatory networks is a significant problem in systems biology. Of particular interest is the problem of determining the unknown or hidden higher level regulatory signals by using gene expression data from DNA microarray experiments. Several studies in this area have demonstrated the critical aspect of the network structure in tackling the network modelling problem. Structural analysis of systems has proved useful in a number of contexts, viz., observability, controllability, fault diagnosis, sparse matrix computations etc. In this contribution, we formally define structural properties that are relevant to Gene Regulatory Networks. We explore the structural implications of certain quantitative methods and explain completely the connections between the identifiability conditions and structural criteria of observability and distinguishability. We illustrate these concepts in case studies using representative biologically motivated network examples. The present work bridges the quantitative modelling methods with those based on the structural analysis. © 2006 IEEE.