  We study the nonclassical correlations in a two-qubit state by the perturbing
local unitary operation method. We find that the definitions of various
non-classicalities including quantum discord (QD), measurement-induced
nonlocality (MIN) and so on usually do not have a unique definition when
expressed as the perturbation of local unitary operations, so a given
non-classicality can lead to different definitions of its dual
non-classicality. In addition, it is shown that QD and MIN are not the
corresponding dual expressions in a simple set of unitary operations, even
though they are in their original definitions. In addition, we also consider
the non-classicalities in general $2\otimes d$ dimensional systems.
