Sifter device for sifting granular material to be sifted, exhibiting - a first V-shaped static cascade sifter, said first cascade sifter exhibiting a first sifting zone with first baffle plates arranged in staircase-like manner and with first sifting fins arranged in louver-like manner, at least one sifting-air inlet for sifting air, at least one charge opening for the granular material to be sifted, at least one discharge opening for a sifted-out coarse-material fraction and also an outlet for a volume flow consisting of the sifting air and a first withdrawn fraction of material to be sifted, and - a second V-shaped static cascade sifter, said second cascade sifter exhibiting a second sifting zone with second baffle plates arranged in staircase-like manner and with second sifting fins arranged in louver-like manner, an inlet for a volume flow of sifting air, at least one discharge opening for a sifted-out coarser fraction of material to be sifted (product A) and an outlet for a volume flow consisting of the sifting air and a second withdrawn, finer fraction of material to be sifted, wherein the volume flow of sifting air of the second cascade sifter is provided by the volume flow consisting of the sifting air and the first withdrawn fraction of material to be sifted from the first cascade sifter, wherein the second V-shaped static cascade sifter is pneumatically connected to the first V-shaped static cascade sifter and is linked downstream of the first cascade sifter, characterized in that - the outlet for the volume flow consisting of the sifting air and the first withdrawn fraction of material to be sifted of the first cascade sifter is provided as a sifting-zone boundary wall of the first cascade sifter, which is permeable to this volume flow and arranged downstream of the first sifting fins in the direction of flow, - the inlet for the volume flow of sifting air of the second cascade sifter is provided as a sifting-zone boundary wall of the second cascade sifter, which is permeable to this volume flow of sifting air and arranged upstream of the second baffle plates in the direction of flow, and wherein - the sifting-zone boundary wall of the first cascade sifter, arranged downstream of the first sifting fins in the direction of flow and the sifting-zone boundary wall of the second cascade sifter, arranged upstream of the second baffle plates in the direction of flow, are spaced from one another, forming a cavity situated between them, and - an outlet opening in a wall of the cavity is provided for branching off a partial volume flow of the volume flow from the first cascade sifter. - a first V-shaped static cascade sifter, said first cascade sifter exhibiting a first sifting zone with first baffle plates arranged in staircase-like manner and with first sifting fins arranged in louver-like manner, at least one sifting-air inlet for sifting air, at least one charge opening for the granular material to be sifted, at least one discharge opening for a sifted-out coarse-material fraction and also an outlet for a volume flow consisting of the sifting air and a first withdrawn fraction of material to be sifted, and - a second V-shaped static cascade sifter, said second cascade sifter exhibiting a second sifting zone with second baffle plates arranged in staircase-like manner and with second sifting fins arranged in louver-like manner, an inlet for a volume flow of sifting air, at least one discharge opening for a sifted-out coarser fraction of material to be sifted (product A) and an outlet for a volume flow consisting of the sifting air and a second withdrawn, finer fraction of material to be sifted, - the outlet for the volume flow consisting of the sifting air and the first withdrawn fraction of material to be sifted of the first cascade sifter is provided as a sifting-zone boundary wall of the first cascade sifter, which is permeable to this volume flow and arranged downstream of the first sifting fins in the direction of flow, - the inlet for the volume flow of sifting air of the second cascade sifter is provided as a sifting-zone boundary wall of the second cascade sifter, which is permeable to this volume flow of sifting air and arranged upstream of the second baffle plates in the direction of flow, and wherein - the sifting-zone boundary wall of the first cascade sifter, arranged downstream of the first sifting fins in the direction of flow and the sifting-zone boundary wall of the second cascade sifter, arranged upstream of the second baffle plates in the direction of flow, are spaced from one another, forming a cavity situated between them, and - an outlet opening in a wall of the cavity is provided for branching off a partial volume flow of the volume flow from the first cascade sifter.