The subject of two-dimensional convection in a binary fluid is treated by analytical methods and through Galerkin models. The analysis will focus on describing the dynamics of convection at onset of convection. Two independent dynamical parameters are present- one more degree of freedom than single fluid convection. We shall derive normal forms for the tricritical bifurcation - describing the transition between a forward and backward pitchfork bifurcation of a two-dimensional array of rolls in a convecting bulk binary fluid mixture. A multiple time perturbation scheme is constructed to fifth order to describe this motion. The coefficients of the equation are determined as a function of the Lewis number (the ratio of the mass to thermal diffusivity). The degenerate Hopf bifurcation is also investigated using a similar perturbative scheme; with a prediction of the coefficients involved. A model system, using a ’minimal representation’ (Veronis 1968) gives rise to a Galerkin truncated scheme (a set of 14 ordinary differential equations). It is claimed that the dynamical character of both the tricritical and degenerate Hopf bifurcation are included in the zoology of the bifurcation behaviour at onset of convection. These and other dynamical aspects of the equations are investigated. In an attempt to improve upon free slip pervious boundaries a projection of the equations is made onto a more appropriate subspace. A comparison with experimental evidence is given.