The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy-Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.