We present lower bounds on the Higgs boson mass in the Standard Model with
three and four fermion generations, SM(3,4), as well as upper bounds on the
lightest Higgs boson mass in the minimal supersymmetric extension of the S
M with three and four generations, MSSM(8,4). Our analysis utilizes the SM(
3,4) renormalization-group-improved one-loop effective potential of the Hig
gs boson to find the upper bounds on the Higgs mass in the MSSM(3,4), while
the lower bounds in the SM(3,4) are derived from considerations of vacuum
stability. All the bounds increase as the degenerate fourth generation mass
increases, providing more room in theory space that respects the increasin
g experimental lower limit of the Higgs mass.