  In this paper, we introduce Fr\'echet quantum supergroups and their
representations. By using the universal deformation formula of the abelian
supergroups R^{m|n} we construct various classes of Fr\'echet quantum
supergroups that are deformation of classical ones. For such quantum
supergroups, we find an analog of Kac-Takesaki operators that are superunitary
and satisfy the pentagonal relation.
