One feature characterizing the transition from prokaryote to eukaryote is the ‘sudden’ appearance of centrioles and their highly structured products, the typical eukaryotic flagella and cilia. These mechanochemical systems appear as fully developed machines, containing some 200 diffierent proteins (Luck et al. 1978) arranged in a remarkably complex organization which has undergone little modification since the advent of the first eukaryotic cells. It is now well established (see, for example, Satir, 1974) that ciliary and flagellar motility is based on a sliding filament mechanism that superficially resembles the far more extensively studied sliding filament system of striated skeletal muscle.The flagellar system, however, appears to be much more complex than the muscle system, because it does not ‘merely’ shorten and generate force, but develops propagating waves and exerts its effects via hydrodynamic interactions with a viscous medium.