The invention relates to a container conveyor device (10) in a packaging machine having a container carrier (13) with a plurality of container receptacles (15). At least two rotary-driven linear conveyors (11, 28) are provided, and the container carrier (13) has at least one engagement part (14) which can be brought into engagement with the linear conveyors (11, 28). Two curved conveyors (20, 34) each have a curved guide track (21, 35) with which at least one projection of the container carrier (13) can be brought into engagement. A plurality of container carriers (13) can be transported along the upper linear conveyor (11) in a row with a mutual first spacing of less than 30 mm and at an average speed V0. The container carriers can be transported along the lower linear conveyor (28) with a mutual second spacing which is greater than the first spacing and at an average speed Vu, where Vu≥1.5 V0.