We present the evaluation of the two-loop O(g(4)M(t)(2)/M-W(2)) effects in the partial widths of the Z(0) boson in the MS scheme and in two different implementations of the on-shell scheme. We observe a clear reduction of the scheme dependence of the predictions. The renormalization procedure and the Heavy Top Expansion employed in the O(g(4)M(t)(2)/M-W(2)) calculations are illustrated in some detail and intermediate results are provided. We discuss the implication of our results on the constraints for the Higgs mass making use of simple interpolating formulas. We find that precision data give M-H < 285 GeV at 95% C.L. taking into account the theory uncertainty. Including also the information from direct search experiments we obtain a 95% upper bound M-H < 335 GeV, (C) 2000 Elsevier Science B.V. All rights reserved.