The paper investigates the structure and propagation of lock-exchange waves of Newtonian (water) and non-Newtonian fluids advancing over a long, sloped bed surface based on 3-D simulations. The non-Newtonian fluids are characterized by a power-law rheology with a consistency index, k, and a rheological index, n. A lock-exchange configuration is considered in which the initial height of the lock fluid above the inclined bed surface making an angle theta with the horizontal is h0. Results are also compared to the limiting case of a dam-break wave over a horizontal plane. For theta > 10 degrees, the front position of the forward propagating surge exhibits an acceleration phase that is well represented by a power-law x_f~ t^gamma, with the exponent gamma increasing monotonically with θ for constant n and decreasing with n for constant theta. Strong air-fluid mixing occurs for some distance behind the front of the forward propagating surge for theta>10 degrees. Past the initial stages of the propagation of the wave, the volume of mixed fluid, Vm, inside Newtonian and non-Newtonian currents increases with the distance traveled by the front following a power law variation (V_m~ x_f^beta) with beta increasing monotonically with theta due to the stronger turbulence generated near the air-fluid interface. The study shows that turbulent Newtonian waves propagating over a sloped surface retain the two-layer (i.e., near-wall shear layer and constant velocity layer) structure observed for Newtonian dam-break waves propagating over a horizontal bed. However, for theta≥ 10 degres, the shape of the velocity profile inside the near-bed layer varies along the wave. Near the lock gate, the velocity increases linearly with the distance from the bed. At sufficiently large distances from the lock gate, a log-law sublayer is still present, but the von Karman constant, κ, decreases from about 0.4 for theta=0 degrees to about 0.25 for theta>10 degrres. Moreover, the relative thickness of the near-bed layer, delta/h (h is the local thickness of the wave current), decreases with θ. For non-Newtonian waves propagating over inclined surfaces with theta≥ 10 degrres, the log-law sublayer is absent at all locations. The velocity variation inside the near-bed layer is close to linear near the lock gate while, away from it, the velocity variation in between the bed and the air-fluid interface is well described by a laminar, steady boundary-layer-type profile for power-law fluids, provided that the rheological index, n, is replaced by a modified rheological index, n’, that is a function of n and theta.