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In the last decade many computational approaches have been introduced to model networks of molecular interactions from gene expression data. Such networks can provide an understanding of the regulatory mechanisms in the cells. System identification algorithms refer to a group of approaches that capture the dynamic relationship between the input and output of a system, and provide a deterministic model of its function. These approaches have been extensively developed for engineering systems, and have reasonable computational requirements. In this paper, we present two system identification methods applied to reverse engineering of gene regulatory networks. Gene regulatory networks are constructed as systems where the output to be estimated is an expression profile of a gene, and the inputs are the potential regulators of that gene. The first reverse engineering method is based on orthogonal search and selects terms from a predefined set of gene expression profiles to best fit the expression levels of a given output gene. The second method consists of multiple cascade models; each cascade includes a dynamic component and a static component. Several cascades are used in parallel to reduce the difference of the estimated expression profiles with the actual ones. To assess the performance of the proposed methods, they are applied to a temporal synthetic dataset, a simulated gene expression time series of songbird brain, and yeast Saccharomyces Cerevisiae cell cycle. Results are compared to known mechanisms of the underlying data and the literature, and demonstrate that the proposed approaches capture the underlying interactions as networks.