A thrust reverser with doors having at least one stationary structure is provided, on which at least one door is mounted pivoting between a closed position in which the door closes the reverser and makes up an outer cowling part, and an open position in which the door opens a passage in the stationary structure and can at least partially block a flow of air generated by a turbojet engine so as to reorient the door. The stationary structure includes at least two sets of cascade vanes that can be covered by the door when in the closed position.