  The term integrable asymptotically conformal at a point for a quasiconformal
map defined on a domain is defined. Furthermore, we prove that there is a
normal form for this kind attracting or repelling or super-attracting fixed
point with the control condition under a quasiconformal change of coordinate
which is also asymptotically conformal at this fixed point. The change of
coordinate is essentially unique. These results generalize K\"onig's Theorem
and B\"ottcher's Theorem in classical complex analysis. The idea in proofs is
new and uses holomorphic motion theory and provides a new understanding of the
inside mechanism of these two famous theorems too.
