The unusual surface-ordered state of liquid n-alkanes was investigated by simulations of a slab of liquid heptadecane with two free surfaces. The results confirm that the surface-ordered state consists of a monolayer of molecules aligned perpendicular to the surface which are mostly in an all trans conformation. The local arrangement of molecules within the monolayer is hexagonal and the density is higher than in the bulk phase. Good agreement was found between the simulation results and X-ray diffraction and reflection data. The simulations showed that there is lateral diffusion within the surface ordered layer, albeit reduced compared to the bulk diffusion, and that there is considerable freedom of motion in the direction perpendicular to the surface. The surface-ordered layer is more like a monolayer of a smectic liquid crystal than a monolayer of solid. A disordered liquid surface at a higher temperature shows no preferred molecular orientation near the surface. The transition between the disordered and ordered phases differs from classical surface freezing in that it is apparently first-order with hysteresis and the thickness does not diverge as the bulk freezing temperature is approached. The simulation results are related to various theories of this transition.