The static mixer (1) includes at least one vane pair (2; 2a, 2b) for the generation of a flow swirl (300) in the direction (30) of a passage flow (3). Edges of the vanes at the front at the leading side are perpendicular to the passage flow and parallel to a height of the passage (10). Onflow surfaces following downstream are bent out in a concave manner and in opposite senses. Each vane (2a, 2b) is formed as an aerodynamically designed body which includes an end wall (20), a convex side wall (21) and a concave side wall (22). The end wall has a convex shape or a shape of a leading edge. The vane cross-sections perpendicular to the side walls in particular have similar shapes to cross-sections of aeroplane wings.