Door system for an aircraft, having a door frame defining a door opening and having a first circumferential strut extending in a circumferential direction and a second circumferential strut extending in the circumferential direction and arranged at a distance from the first circumferential strut with respect to a longitudinal direction extending transversely to the circumferential direction; at least one first frame stopper fixed to the first circumferential strut and at least one second frame stopper fixed to the second circumferential strut, the frame stoppers (31; 32) each have a first abutment section projecting into the door opening and having a first toothing, the first toothings each being formed at an inner surface of the first abutment section, which inner surface extends perpendicularly to a radial direction extending transversely to the longitudinal direction and transversely to the circumferential direction; a door movably mounted relative to the door frame and arranged in a closed state in the door opening; and a number of door stoppers (51; 52) corresponding to the number of the frame stoppers (31; 32) which door stoppers (51; 52) are arranged on opposite sides (41; 42) of the door and are connected to the door and which each have a second abutment section, wherein the second abutment section has a second toothing formed complementarily to the first toothing, and wherein the first toothing of a respective frame stopper (31; 32) and the second toothing of a respective door stopper (51; 52) engage in one another in the closed state of the door; wherein the first toothing and the second toothing have a plurality of engagement elements or toothed elements. a door frame defining a door opening and having a first circumferential strut extending in a circumferential direction and a second circumferential strut extending in the circumferential direction and arranged at a distance from the first circumferential strut with respect to a longitudinal direction extending transversely to the circumferential direction; at least one first frame stopper fixed to the first circumferential strut and at least one second frame stopper fixed to the second circumferential strut, the frame stoppers (31; 32) each have a first abutment section projecting into the door opening and having a first toothing, the first toothings each being formed at an inner surface of the first abutment section, which inner surface extends perpendicularly to a radial direction extending transversely to the longitudinal direction and transversely to the circumferential direction; a door movably mounted relative to the door frame and arranged in a closed state in the door opening; and a number of door stoppers (51; 52) corresponding to the number of the frame stoppers (31; 32) which door stoppers (51; 52) are arranged on opposite sides (41; 42) of the door and are connected to the door and which each have a second abutment section, wherein the second abutment section has a second toothing formed complementarily to the first toothing, and wherein the first toothing of a respective frame stopper (31; 32) and the second toothing of a respective door stopper (51; 52) engage in one another in the closed state of the door; wherein the first toothing and the second toothing have a plurality of engagement elements or toothed elements.