The equations and numerics necessary for the analysis of dense-gas boundary-layer flows over arbitrarily shaped two-dimensional bodies are developed. The governing equations are derived from the Navier-Stokes-Fourier equations for a general fluid. A numerical method based on the second-order Davis-coupled scheme is employed to solve for mean flows over flat plates. Flows of nitrogen, sulfur hexafluoride, and toluene over adiabatic walls are examined; in addition, flows of nitrogen over heated and cooled walls are studied. Results indicate a breakdown of the standard correlations for the recovery factor and the Nusselt number due primarily to the substantial variations of the Prandtl number and the Chapman-Rubesin parameter throughout the boundary layer. The stability equations for two-dimensional inviscid disturbances in a general fluid are derived. The temporal stability of the mean flows of nitrogen is subsequently examined using the generalized inflection-point criterion extracted from these equations. Results reveal significant variations from standard ideal-gas predictions including the existence of flows for which neither heating nor cooling of the wall has a stabilizing effect.