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Measurements of the nonlinear flux-flow resistivity $\ensuremath{\rho}$ and the critical vortex velocity ${v}_{\ensuremath{\varphi}}^{*}$ at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov (Z. Eksp. Teor. Fiz 68, 1915 (1975) [Sov. Phys. JETP 41, 960 (1976)]) are reported along the node and antinode directions of the $d$-wave order parameter in the $a\mathrm{\text{\ensuremath{-}}}b$ plane of epitaxial ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ films. In this pinning-free regime, $\ensuremath{\rho}$ and ${v}_{\ensuremath{\varphi}}^{*}$ are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of $\ensuremath{\rho}$ is almost independent of temperature and field. We attribute the observed results to the anisotropic quasiparticle distribution on the Fermi surface of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$.