This paper presents a new constraint on the strongly interacting Higgs sector based on precision weak-interaction measurements. The authors show that the Higgs sector must have an approximate global SU(2) 'custodial' symmetry, as implied by the relation between the W and Z boson masses and the weak mixing angle. They also demonstrate that precision weak interaction experiments constrain an isospin-symmetric observable of the Higgs sector. The analysis is based on the general formalism for weak interaction radiative corrections, which shows that new physics beyond the standard model primarily affects vacuum polarization amplitudes. The authors consider the effects of a heavy top quark and technicolor models, where the Higgs sector is a copy of the usual strong interactions scaled up to TeV energies. In such models, the Higgs sector conserves isospin and parity, and the vacuum polarization amplitudes of weak isospin currents are divided into contributions from vector and axial-vector currents. The authors compute the values of S and T, which are parameters that characterize the Higgs sector, and find that they are generally positive and tend to compensate each other in any single observable. The results show that the technicolor models with two generations of technifermions are excluded, but not yet those with a single generation. The authors conclude that future experiments at LEP and SLC will provide more accurate measurements of the Higgs sector, which will help to constrain its properties.This paper presents a new constraint on the strongly interacting Higgs sector based on precision weak-interaction measurements. The authors show that the Higgs sector must have an approximate global SU(2) 'custodial' symmetry, as implied by the relation between the W and Z boson masses and the weak mixing angle. They also demonstrate that precision weak interaction experiments constrain an isospin-symmetric observable of the Higgs sector. The analysis is based on the general formalism for weak interaction radiative corrections, which shows that new physics beyond the standard model primarily affects vacuum polarization amplitudes. The authors consider the effects of a heavy top quark and technicolor models, where the Higgs sector is a copy of the usual strong interactions scaled up to TeV energies. In such models, the Higgs sector conserves isospin and parity, and the vacuum polarization amplitudes of weak isospin currents are divided into contributions from vector and axial-vector currents. The authors compute the values of S and T, which are parameters that characterize the Higgs sector, and find that they are generally positive and tend to compensate each other in any single observable. The results show that the technicolor models with two generations of technifermions are excluded, but not yet those with a single generation. The authors conclude that future experiments at LEP and SLC will provide more accurate measurements of the Higgs sector, which will help to constrain its properties.