Steady supersonic flows around a corner are studied theoretically for a dusty gas in which the gas and the particles make a significant exchange of momentum and heat. Perfect-gas theory for the dusty gas in an equilibrium limit is used to examine the nature of the flow far from the corner. The maximum flow-deflection angle is found to be increased by the presence of the particles. The equations of motion are solved numerically to study the transition of the flow from a frozen state at the corner to a near-equilibrium state at infinity. The differences in nonequilibrium properties of the flow between the cases of large and small deflection angles of the corner are discussed. Numerical results for large deflection angles show that the gas expands excessively after it enters a pure-gas region which forms along the wall surface. In every case, diffusive flow patterns arise around the effective wavehead and wavetail in the far field. It is shown analytically that the length of the diffusive flow domain increases in proportion to the square root of the distance from the wall.