A conveyor system adapted to handle a bottle having a neck portion provided with a bead (Vb), a cylindrical portion (Vc) and a flange (Vf) in this order below a thread (Vt), the conveyor system comprising: an upstream machine adapted to support the downward-facing side of the flange (Vf) to transport the bottle along its circumference; an intermediate wheel adapted to receive the bottle from the upstream machine and transports the bottle along its circumference while gripping the neck portion of the bottle to suspend the bottle; a downstream machine adapted to receive the bottle from the intermediate wheel and to transport the bottle along its circumference while gripping the downward-facing side of the flange (Vf); the intermediate wheel includes a plurality of grippers (30, 60) along its circumference, the gripper (30, 60) being adapted to grip the neck portion of the bottle by a pair of pivotal gripping members (30A, 60A); and the gripper (30, 60) of the intermediate wheel comprises, common contact parts (Q1, Q2) provided on each gripper member (30A, 60A) and adapted to come into contact with the neck portion when the gripper (30, 60) is gripping either of a first bottle or a second bottle, wherein a diameter of the neck portion of the second bottle is larger than that of the first bottle; and a large-diameter bottle contact part adapted to be separated from the neck portion when gripping the first bottle and to abut the neck portion when gripping the second bottle; the common contact parts (Q1, Q2) are configured to engage with a lower surface of the bead (Vb) and an upper surface of the flange (Vf) when gripping the first bottle; the large-diameter bottle contact part is configured to engage with at least the upper surface of the flange (Vf) when gripping the second bottle; said conveyor system being characterised in that the thickness of the gripping member (30A, 60A) at the large-diameter bottle contact part is strictly higher than the thickness of the gripping member (30A, 60A) at the common contact parts (Q1, Q2) and in that the common contact parts (Q1, Q2) are configured to engage with a lower surface of the bead (Vb) and configured to be away from the upper surface of the flange (Vf) when gripping the second bottle. an upstream machine adapted to support the downward-facing side of the flange (Vf) to transport the bottle along its circumference; an intermediate wheel adapted to receive the bottle from the upstream machine and transports the bottle along its circumference while gripping the neck portion of the bottle to suspend the bottle; a downstream machine adapted to receive the bottle from the intermediate wheel and to transport the bottle along its circumference while gripping the downward-facing side of the flange (Vf); the intermediate wheel includes a plurality of grippers (30, 60) along its circumference, the gripper (30, 60) being adapted to grip the neck portion of the bottle by a pair of pivotal gripping members (30A, 60A); and the gripper (30, 60) of the intermediate wheel comprises, common contact parts (Q1, Q2) provided on each gripper member (30A, 60A) and adapted to come into contact with the neck portion when the gripper (30, 60) is gripping either of a first bottle or a second bottle, wherein a diameter of the neck portion of the second bottle is larger than that of the first bottle; and a large-diameter bottle contact part adapted to be separated from the neck portion when gripping the first bottle and to abut the neck portion when gripping the second bottle; the common contact parts (Q1, Q2) are configured to engage with a lower surface of the bead (Vb) and an upper surface of the flange (Vf) when gripping the first bottle; the large-diameter bottle contact part is configured to engage with at least the upper surface of the flange (Vf) when gripping the second bottle; said conveyor system being characterised in that the thickness of the gripping member (30A, 60A) at the large-diameter bottle contact part is strictly higher than the thickness of the gripping member (30A, 60A) at the common contact parts (Q1, Q2) and in that the common contact parts (Q1, Q2) are configured to engage with a lower surface of the bead (Vb) and configured to be away from the upper surface of the flange (Vf) when gripping the second bottle.