  This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine
and geominimal surface areas for star bodies, which belong to the recent dual
Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new
affine invariants will be provided. Moreover, related Orlicz affine
isoperimetric inequality, cyclic inequality, Santal\'{o} style inequality and
Alexander-Fenchel type inequality are established.
