  We present a consistent \delta N formalism for curvature perturbations in
anisotropic cosmological backgrounds. We employ our \delta N formalism to
calculate the power spectrum, the bispectrum and the trispectrum in models of
anisotropic inflation with the background gauge fields in Bianchi I universe.
Our results coincide exactly with the recent results obtained from in-in
formalism. To satisfy the observational constraints the anisotropies generated
on power spectrum are kept small but large orientation-dependent
non-Gaussianities can be generated. We study the Suyama-Yamaguchi inequality
for the amplitudes of the bispectrum and the trispectrum in the presence of
anisotropic shapes.
