Abstract: A seal device for sealing between a wall (3) and a shaft (5), especially in a pump, comprising a stationary, preferably ceramic, seal element (13), which is connected to the wall, and a movably, preferably ceramic, seal element (14) which is connected to the shaft and which seals against the stationary seal element. At least one of the seal elements is attached directly to a holding member (12), which is connected to the wall alternatively to the shaft. The seal element (13) of the holding member is provided with a circumferential surface (18), which, in the alternative in which the holding member is connected to the wall, extends in the hole (7) of the wall (3) in such a manner that an annular gap is formed between the wall and said circumferential surface. An elastic sealing ring (20) is provided in said gap for sealing between the wall and the seal element of the holding member.