In this paper we study a Landau–de Gennes model of a nematic liquid crystal in a model shear flow employing a range of analytical and numerical techniques. We use asymptotic methods and numerical bifurcation theory to provide a comprehensive description of the different in–plane modes that exist in terms of the temperature and imposed shear rate, as well as determining their stability to in–plane disturbances. We show that there are two physically distinct solution branches, one of which corresponds to an in–plane director (denoted IPN). The other branch corresponds to the director being aligned perpendicular to the shear plane, i.e. so–called log–rolling states. We find both tumbling and wagging time–dependent modes. The mode structure is organized by a Takens–Bogdanov point, at which a family of Hopf bifurcation points and a family of limit points coincide. At low strain rates tumbling occurs as a transition from the IPN branch. In addition, we show that at larger values of the strain rate the wagging modes emanate from a Hopf bifurcation on the IPN branch and evolve continuously into tumbling modes. Moreover, we show analytically that this boundary between tumbling and wagging corresponds to a state in which the distribution function is cylindrical in the shear plane. This provides confirmation of the tumbling–wagging transition mechanism observed by Tsuji and Rey in numerical calculations relating to a confined geometry.