SM Higgs mass bounds from theory

The two-loop Higgs mass upper bounds are reanalyzed. Previous results for a cutoff scale $\Lambda\approx$ few TeV are found to be too stringent. For $\Lambda=10^{19}$ GeV we find $M_H < 180 \pm 4\pm 5$ GeV, the first error indicating the theoretical uncertainty, the second error reflecting the experimental uncertainty due to $m_t = 175 \pm 6$ GeV. We also summarize the lower bounds on $M_H$. We find that a SM Higgs mass in the range of 160 to 170 GeV will certainly allow for a perturbative and well-behaved SM up to the Planck-mass scale $\Lambda_{Pl}\simeq 10^{19}$ GeV, with no need for new physics to set in below this scale.