The generalized S 2 -transform of a member of f of a certain space of generalized functions is defined as F ( x ) = 〈 f ( t ) , k ( x , t ; ρ ) 〉 ,  where k ( x , t ; ρ ) = ∫ 0 ∞ 1 ( x + y ) ρ ( y + t ) ρ   d y ,   ρ > 1 2 , 0 < x < ∞   and   0 < t < ∞ . An inversion theorem for the transform is established interpreting the oonvergene in the weak distributional sense.