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We aim at developing a new methodology to model and design periodic oscillators of gene regulatory networks with multiple genes, proteins and time delays, by using multiple time-scale networks (MTN). Multiple time scale properties are exploited to simplify the model according to singular perturbation theory. We show that a MTN has no stable equilibria but stable periodic orbits. Finally, we design a biologically plausible gene oscillator by cI and Lac genes, to demonstrate our theoretical results.