Measurements of the nonlinear flux-flow resistivity $rho$ and the critical vortex velocity $rm v^*_phi$ at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov cite{LO} are reported along the node and antinode directions of the d-wave order parameter in the textit{a-b} plane of epitaxial $YBa_2Cu_3O_{7-delta}$ films. In this pinning-free regime, $rho$ and $rm v^*_phi$ are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of $rho$ is almost independent of temperature and field. We attribute the observed results to the anisotropic quasiparticle distribution on the Fermi surface of $YBa_2Cu_3O_{7-delta}$.