A thrust reverser device for an aircraft motor nacelle comprising: - a cowl (10, 21) movable in reciprocation between a deployed position in which it opens a passage in the nacelle, said position being adapted to allow a reverse jet operation of said nacelle, and a retracted position in which it closes this passage, said position being adapted to allow a direct jet operation of the nacelle; - a cascade vane assembly of a secondary air flow flowing in a circulation flow path of the secondary air flow of the nacelle, fastened upstream of said cowl; - blocking flaps of the secondary air flow alternately movable between: ∘ a folded position in which said flaps are stowed, at least for a retracted position of said cowl inside said cowl and under said cascade vane assembly, and ∘ a deployed position in which they block at least partially the secondary air flow flowing in said flow path, - means for performing the switch from a direct jet operation to a reverse jet operation, adapted to carry out the switch from a direct jet operation to a reverse jet operation in two phases: ∘ translation of the movable cowl downstream of the nacelle to a deployed position of said cowl, said flaps being in folded position, ∘ opening of the blocking flaps from said folded position to said deployed position, said thrust reverser device being characterized in that the blocking flaps include an upstream edge mounted on a hinge secured to said cascade vane assembly and a downstream edge mounted on a lever hinged on said cascade vane assembly. - a cowl (10, 21) movable in reciprocation between a deployed position in which it opens a passage in the nacelle, said position being adapted to allow a reverse jet operation of said nacelle, and a retracted position in which it closes this passage, said position being adapted to allow a direct jet operation of the nacelle; - a cascade vane assembly of a secondary air flow flowing in a circulation flow path of the secondary air flow of the nacelle, fastened upstream of said cowl; - blocking flaps of the secondary air flow alternately movable between: ∘ a folded position in which said flaps are stowed, at least for a retracted position of said cowl inside said cowl and under said cascade vane assembly, and ∘ a deployed position in which they block at least partially the secondary air flow flowing in said flow path, ∘ a folded position in which said flaps are stowed, at least for a retracted position of said cowl inside said cowl and under said cascade vane assembly, and ∘ a deployed position in which they block at least partially the secondary air flow flowing in said flow path, - means for performing the switch from a direct jet operation to a reverse jet operation, adapted to carry out the switch from a direct jet operation to a reverse jet operation in two phases: ∘ translation of the movable cowl downstream of the nacelle to a deployed position of said cowl, said flaps being in folded position, ∘ opening of the blocking flaps from said folded position to said deployed position, ∘ translation of the movable cowl downstream of the nacelle to a deployed position of said cowl, said flaps being in folded position, ∘ opening of the blocking flaps from said folded position to said deployed position,