  In this letter we show that in the extra dimension model, contrary to the
widely accepted conception, the simply truncated $\phi^4$ and non-Abelian SU(N)
Kaluza-Klein theories are not renormalizable, i.e. the tree level relations of
the effective theories can not sustain the quantum corrections. The breaking
down of the tree level relations of the effective theories can be traced back
to several factors: the breaking of the higher dimension Lorentz symmetry and
higher dimension gauge symmetry, interactions assumed in the underlying
Lagrangians, and the dimension reduction and rescaling procedure.
