In stunning of slaughter animals by means of a box stunning apparatus with stunning atmosphere, boxes (1, 1a, 1b, 1c, 1d) are conveyed around after one another to various stop positions by means of a transport system (11, 12). Animals to be stunned are driven forwards in a driveway (2) and into an entrance area (3). The animals in the entrance area are separated from other animals after a group of animals has passed into the area. The group is driven into an empty box (1) that is brought to a halt in the first stop position at the entrance area. The box is then conveyed into the stunning atmosphere. After the animals have been in the atmosphere the box is conveyed out of the atmosphere and is brought to a stop at an emptying area (13) to empty the box of stunning animals.