The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small, but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit-cycle reconstruction.We report a quality factor of flagellar oscillations, Q = 38.0 ± 16.7 (mean±s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems. Here, we report direct measurements of phase and amplitude fluctuations of the flagellar beat and discuss the microscopic origin of active flagellar fluctuations using a minimal model. We further illustrate the impact of flagellar fluctuations on swimming and synchronization. Our analysis contributes to a recent interest in driven, outof-equilibrium systems and their fluctuation fingerprint [15][16][17][18] by characterizing noisy limit-cycle dynamics in an ubiquitous motility system, the flagellum.Flagellar shape analysis. We characterize flagellar beat patterns as superposition of principal shape modes. This dimensionality reduction is key to our fluctuation analysis. We analyze planar beat patterns of bull sperm swimming close to a boundary surface [19], filmed at 250 frames-per-second (corresponding to about 8 frames per beat cycle). The flagellar centerline r(s, t), tracked as function of arclength position s and time t, can be expressed with respect to a material frame of the sperm head in terms of a tangent angle ψ(s, t)Here, r h (t) denotes the sperm head center, and e 1 and e 2 are ortho-normal vectors with e 1 pointing along the long head axis, see Fig. 1A. A space-timeplot of ψ(s, t) reveals the periodicity of the flagellar beat, see Fig. 1B. This high-dimensional data set can be projected on a low dimensional 'shape space' using shape mode analysis based on principal component analysis [20]. The time-averaged tangent angle ψ 0 (s)= n i=1 ψ(s, t i )/n characterizes the mean shape of the beating flagellum (n=1024 frames in each movie). We further define a two-point correlation matrix arXiv:1401.7036v2 [q-bio.CB]