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This article discusses the finite-time stability problem for stochastic genetic regulatory networks (SGRNs) with time-varying delays. By designing suitable adaptive controllers and skillfully choosing appropriate Lyapunov and multi-Lyapunov functions, respectively, the above non-switched and switched SGRNs can achieve finite time stability in probability. Superior to some existing controllers for GRNs, the above adaptive design procedures can reduce the dependence of the system parameters. Finally, two numerical simulation examples illustrate the effectiveness of the theoretical results.