This study focuses on numerically analyzing the transition from periodic to chaotic dynamics in the fluid-elastic response of a 2-dof flexibly-mounted airfoil with chord-wise rigidity. The computational framework is composed of a high fidelity Navier–Stokes solver, weakly coupled with a structural model having geometric nonlinearity represented by cubic order stiffness terms. A low Reynolds number flow regime and a very low structure-to-fluid added mass ratio have been considered to simulate the flying conditions of very light-weight unmanned devices. A bifurcation analysis of the system, in the absence of actuation or control forces, is undertaken with the wind velocity as the control parameter. The route to chaos – identified to be the Ruelle–Takens–Newhouse quasi-periodic route – is established for the first time for a flexible pitch–plunge flapping system. Robust nonlinear time series analysis techniques have been implemented to characterize different complex dynamical states present in the system. © 2018 Elsevier Ltd