[en] The fixed point structure of the renormalization group equations for the scalar quartic couplings in the one and two-doublet models is studied. Masses of the physical Higgs bosons can be determined by the infrared fixed points of the quartic coupling constants. The existence of these fixed points in the two-doublet model requires the presence of a heavy fourth generation in which quarks are coupled to both doublets. Otherwise, the potential can become quartically unstable at low energies for arbitrary initial stable values of the coupling constants. 9 refs., 5 figs