The two-parametric quantum deformation of the algebra of coordinate functions on the (dual) supergroup Gr(1\1) via a contraction of Gr(p,q) (1\1) is presented. Although the quantum superdeterminant of any element of Gr(p,q) (1\1) is not central, in the two parametric Jordanian deformation of Gr(1\1) the quantum superdeterminant belongs to the center. The Hopf algebra structure of Gr(h1), (h2) (1\1) is discussed. (C) 1999 American Institute of Physics. [S0022-2488(99)00606-4].