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

Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas