Modern experimental techniques for the quantitative, time-course measurement of protein concentrations and gene activation levels enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appropriate network structures to the data along with the corresponding network parameters. For a given set of genes, exploring all possible network structures is clearly prohibitive. Modelling approaches and identification techniques selecting a priori the network structures compatible with biological knowledge and the available experimental data are necessary to make the identification problem tractable. We propose a dynamic modelling framework based on differential equations where the logical structure of interactions among genes is captured by a class of Boolean rules known as hierarchically canalizing functions. We establish analytical properties of the resulting dynamical equations which are independent of the specific model in the class and of its parameters, and devise a low complexity procedure that isolates hierarchies of model structures compatible with time series of gene product concentrations and synthesis rates. We then construct an identification procedure that returns a pool of best fitting model structures along with estimates of their parameters. We test the method on simulated data of a synthetic network and a realistic model of Escherichia coli nutrients stress response.