The swimming behavior of Bacteria has been studied extensively, at least for some species like Escherichia coli. In contrast, almost no data have been published for Archaea on this topic. In a systematic study we asked how the archaeal model organisms Halobacterium salinarum, Methanococcus voltae, Methanococcus maripaludis, Methanocaldococcus jannaschii, Methanocaldococcus villosus, Pyrococcus furiosus, and Sulfolobus acidocaldarius swim and which swimming behavior they exhibit. The two Euryarchaeota M. jannaschii and M. villosus were found to be, by far, the fastest organisms reported up to now, if speed is measured in bodies per second (bps). Their swimming speeds, at close to 400 and 500 bps, are much higher than the speed of the bacterium E. coli or of a very fast animal, like the cheetah, each with a speed of ca. 20 bps. In addition, we observed that two different swimming modes are used by some Archaea. They either swim very rapidly, in a more or less straight line, or they exhibit a slower kind of zigzag swimming behavior if cells are in close proximity to the surface of the glass capillary used for observation. We argue that such a "relocate-and-seek" behavior enables the organisms to stay in their natural habitat.