Herein work is researching extremes asymptotic of Pareto random values. Here is analyzing geometrically maximum (minimum) stability tasks, also asymptotically tasks, when succession value is geometrical and geometrically stability of lower extremes. Aim of this work is to check if Pareto distribution values are stable maximum and minimum distributions and to continue researches in the area of lower extremes structures. It was proved that maximum (minimum) distribution (when ) is geometrically stable maximum (minimum) distribution, while others – asymptotically k-stable. When , maximum (minimum) distribution is asymptotically stable, only maximum distribution is also Pareto distribution, but with the displacement, while other - asymptotically k-stable.