Laboratory experiments are presented from a modelling investigation into the influence of shelf and slope topography on f-plane surface and intermediate flows along ocean boundaries. The surface flows are formed from an upstream source by the release of fresh water into a rotating tank containing salt water, while for the intermediate-water counterpart flows, neutrally-buoyant fluid was released from a submerged source into stably-stratified (two-layer) and quiescent receiving waters in solid body rotation. It is shown that the stability of these buoyancy-driven currents can be described satisfactorily by a combination of the dimensionless parameters Bu= N 2/ f 2, Ek=2 ν/ fD 0 2 and Ro= U 0/ fL 0, where N and f are the buoyancy and Coriolis frequencies respectively, D 0, L 0 and U 0 are the initial depth, width and velocity of the currents, respectively, and ν is the kinematic viscosity of the fluid. Furthermore, comparison with physical models of surface and intermediate flows along a vertical wall and over a flat bottom reveals that the stability regimes are not significantly altered by the presence of shelf topography. Variation of the depth of the surface flows with respect to the total fluid depth above the underlying shelf is shown to have a significant effect on the velocity and density structure of these flows. When the depth and width ratios are small, the surface flow is not affected by the varying topography. However, when the current occupies a considerable height above the shelf and is at least as wide as the shelf, upper layer fluid is transported offshore through the bottom Ekman layer, where it is arrested above the sloping bottom. At this location, a deepening of the upper layer develops due to potential vorticity conservation of the lower layer, accompanied by a local alongshore velocity maximum. This shelf break front prevents significant offshore transport of upper layer fluid far beyond the shelf break, even in cases where the flow is unstable. Comparison of the intermediate currents with dynamically-similar currents above a flat bottom does not reveal a stabilising effect of the slope. For unstable intermediate currents, offshore transport is not prohibited (as it is shown to be for surface currents over narrow shelves, due to the presence of the slope), and large scale instability patterns can extend over great distances from the slope. It is shown that the geostrophic nature of these currents is destroyed close to the sloping bottom. Here, the upper and lower density interfaces, denoting the vertical extents of the intermediate current, tilt sharply downwards.