A downstream guide device that is designed for arrangement in a downstream flow of an impeller of an axial fan, wherein the downstream guide device has a housing and a plurality of downstream guide vanes, each of which is connected to the housing and each of which has a leading edge (6.1) and a trailing edge (6.2), wherein each of the downstream guide vanes extends in the radial direction relative to an axis of rotation of the impeller of the axial fan from an inner radius η to an outer radius r a, wherein each of the downstream guide vanes is embodied as a NACA airfoil in cross section, which is defined at least by the maximum airfoil camber f, position of maximum camber x f, airfoil thickness d, and position of maximum thickness x d thereof, wherein each of the downstream guide vanes has an extent L ax,N along an axial direction z of the axial fan parallel to the axis of rotation, wherein the orientation of each of the downstream guide vanes is defined by an angle of attack α, which is the angle between a plane orthogonal to the axis of rotation and an airfoil chord (6.5) of the downstream guide vane, wherein the maximum airfoil camber f, the position of maximum camber x f, the airfoil thickness d, the position of maximum thickness x d, the angle of attack α, and the extent L ax,N of each of the downstream guide vanes are adapted at predetermined intervals along the radial direction from the inner radius η to the outer radius r a to a predetermined operating point or operating range of the axial fan and to the flow generated at the operating point or in the operating range of the impeller, wherein at least the maximum airfoil camber f, the position of maximum camber xr, the airfoil thickness d, the position of maximum thickness x d, the angle of attack α, or the extent L ax,N of a downstream guide vane varies at least in some portions along its course in the radial direction, and wherein transitions between the portions of a follower vane are designed to be smooth, and wherein the respective leading edge (6.1) of each of the downstream guide vanes is multiply curved. the downstream guide device has a housing and a plurality of downstream guide vanes, each of which is connected to the housing and each of which has a leading edge (6.1) and a trailing edge (6.2), wherein each of the downstream guide vanes extends in the radial direction relative to an axis of rotation of the impeller of the axial fan from an inner radius η to an outer radius r a, wherein each of the downstream guide vanes is embodied as a NACA airfoil in cross section, which is defined at least by the maximum airfoil camber f, position of maximum camber x f, airfoil thickness d, and position of maximum thickness x d thereof, wherein each of the downstream guide vanes has an extent L ax,N along an axial direction z of the axial fan parallel to the axis of rotation, wherein the orientation of each of the downstream guide vanes is defined by an angle of attack α, which is the angle between a plane orthogonal to the axis of rotation and an airfoil chord (6.5) of the downstream guide vane, wherein the maximum airfoil camber f, the position of maximum camber x f, the airfoil thickness d, the position of maximum thickness x d, the angle of attack α, and the extent L ax,N of each of the downstream guide vanes are adapted at predetermined intervals along the radial direction from the inner radius η to the outer radius r a to a predetermined operating point or operating range of the axial fan and to the flow generated at the operating point or in the operating range of the impeller, wherein at least the maximum airfoil camber f, the position of maximum camber xr, the airfoil thickness d, the position of maximum thickness x d, the angle of attack α, or the extent L ax,N of a downstream guide vane varies at least in some portions along its course in the radial direction, and wherein transitions between the portions of a follower vane are designed to be smooth, and wherein the respective leading edge (6.1) of each of the downstream guide vanes is multiply curved.