  Electroweak theory with two massless Higgs doublets is studied by solving
renormalization group equations for coupling constants in one-loop
approximation. A cutoff~$\Lambda$, at which one of quartic couplings in the
Higgs potential blows up, is obtained by imposing constraints from the oblique
parameter $T$ on the quartic couplings at low energy. We find $\Lambda \simeq
0.52\sim 8.4$~TeV at the Higgs mass $M_H=100$ GeV. The cutoff $\Lambda$ is at
most about $60$ TeV even if we take into account the LEP lower bound of
$M_H\simeq 64$ GeV. It cannot reach the Planck or GUT scale due to severe
experimental constraints. It is impossible in the model to realize a large
gauge hierarchy as suggested many years ago by S. Weinberg.
