In the field of systems and synthetic biology there has been an increasing interest for the use of genetic circuits during the last decade. Several circuits have been successfully put together, many of which were based on models. During this thesis a model for a toggle switch was analysed both deterministically and stochastically.The HOM2-circuit approximation for a bistable tuneable switch from Ghim and Almaas (2009) was re-derived in order to make it asymmetrical. Deterministic analysis was conducted yielding stability diagrams, describing the phase plane showing bistability for the genetic switch. Furthermore, stochastic simulations of the approximation were conducted. This gave a somewhat narrower bistable area than the deterministic analysis, possibly due to the nature of saddle-node bifurcations. Parameter values for a switch based on experiments were estimated for the approximation, and these were used in a stochastic simulation. The result from this simulation was in correspondencewith the deterministic analysis. A stochastic simulation of the complete circuit was conducted based on parameter values found in literature. For this simulation bistability was not shown.In order to further explore the circuit, and validity of the approximation, experimental investigation is needed. This has been planned together with Rahmi Lale, PhD, and Professor Eivind Almaas at the Department of Biotechnology, NTNU.