  As a generalization of anti-invariant $\xi^\perp-$Riemannian submersions, we
introduce conformal anti-invariant $\xi^\perp-$submersions from almost contact
metric manifolds onto Riemannian manifolds. We investigate the geometry of
foliations which are arisen from the definition of a conformal submersion and
find necessary and sufficient conditions for a conformal anti-invariant
$\xi^\perp-$submersion to be totally geodesic and harmonic, respectively.
Moreover, we show that there are certain product structures on the total space
of a conformal anti-invariant $\xi^\perp-$submersion.
