Cilial and flagella are motile organelles that propel cells through aqueous media or move aqueous media across cells. Motion is driven by an oscillatory, serpentine beating waveform of the slender rod-like organelles. The beating pattern arises from forces generated by the motor proteins dynein that cause shear between the microtubules within the cilia and flagella. Motor activity is coordinated in two ways: (i) across the axis so that motors on one side are active while motors on the other side are not, and (ii) along the length so that motors at a given location become sequentially active and then inactive as the bend passes this location. We hypothesize that coordination is due to mechanical signaling between the dynein motors (Howard, Ann. Rev. Biophys., 2009). Combined with the bending stiffness of the microtubules (which tends to return the axoneme to its straight conformation), and delays associated with signaling (which result in "chemical inertia"), the system is capable of oscillations. We have shown that such a system can account very well for the serpentine beat of bull sperm when the hydrodynamic drag from the surrounding fluid is taken into account (Riedel-Kruse et al. HSFP Journal, 2007). We are now testing our mechanical model for the axonemal beat using the cilia of the single-cell alga Chlamydomonas reinhardtii.