  We analyze the two loop renormalization group equations in the standard model
and its extensions for the coupling constants and the quark Yukawa couplings.
The key point of our analysis is the observed hierarchy of the quark masses and
the CKM matrix. For the one loop evolution we find the explicit solution for
the evolution of the Yukawa couplings and show the following: 1. the CKM matrix
depends on the energy on only one function of energy; 2. the ratios of the down
quark masses depend on the energy through the same function as the CKM matrix;
3. the diagonalizing matrices of the biunitary transformation of the up quarks
are energy independent. Next we give the explicit form of the two loop
corrections to the evolution of the quark Yukawa couplings and show that the
relative corrections are of the order (\lambda ^{4}) for the quark Yukawa
couplings and of the order (\lambda ^{5}) for the CKM matrix. Finally we give
the equations of the one loop evolution of the squares of the matrix elements
of the CKM matrix and their explicit solution.
