The study reports the quasi-periodic flowdynamics behind a spanwise flexible flapping airfoil. In the qualitative transition in the unsteady flowfield, the trailing-edge wake loses its periodicity beyond a critical wind velocity and becomes quasi-periodic (QP) in nature. The quasi-periodic state is observed at a regime of comparable solid and fluid added mass. The quasi-periodicity of the wake is observed qualitatively by phase-averaged vorticity contours. Quantitative evidence of the dynamical transition has been presented using flowfield quantity vorticity as well as the time evolution of the aerodynamic loads. The correlation coefficient of the vorticity field and the reconstructed phase space, frequency spectra, PoincareÁ sections, and recurrence plots of the aerodynamic loads establish the presence of quasi-periodicity in the flow topology conclusively. The loss of periodicity is shown to lead to variability in the aerodynamic loads at the corresponding flow regimes, implying the potential requirement of feedback control mechanisms for stable operations at these flow regimes.