Buoyancy driven flows of two Bingham fluids in an inclined slot are considered, providing a simplified model for the plug cementing process. The flows studied are near-uniaxial and stratified, with the heavy fluid moving down the incline, displacing the lighter fluid upwards. There is no net axial volume flux. Four qualitatively different types of velocity solution profiles, u, are shown to exist, three of which are non-trivial. The regions of existence of each flow type can be described parametrically in terms of the two dimensionless fluid yield stresses, (tau(c,Y), tau(m,Y)), and the dimensionless interface height in the slot, h. The boundary of the region in the (tau(c,Y), tau(m,Y)) plane, outside of which only the trivial solution u=0 exists, is determined exactly and a simple analytic expression is given. Within this region, perturbation methods are used to produce asymptotic approximations to the flow rates and interface velocities for values of h such that u not equal 0. The perturbation solutions are used to study axial propagation of the interface height profile h(x, t) along the slot.