The azimuthal anisotropy coefficients v2 and v4 of π 0 and η mesons are measured in Au+Au collisions at √ sNN = 200 GeV as a function of transverse momentum pT (1-14 GeV/c) and centrality.The extracted v2 coefficients are found to be consistent between the two meson species over the measured pT range. The ratio of v4/v 2 2 for π 0 mesons is found to be independent of pT for 1-9 GeV/c, implying a lack of sensitivity of the ratio to the change of underlying physics with pT . Furthermore, the ratio of v4/v 2 2 is systematically larger in central collisions, which may reflect the combined effects of fluctuations in the initial collision geometry and finite viscosity in the evolving medium.