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 th
e Heavy Top Expansion employed in the O(g(4)M(t)(2)/M-W(2)) calculations ar
e illustrated in some detail and intermediate results are provided. We disc
uss the implication of our results on the constraints for the Higgs mass ma
king 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. Incl
uding also the information from direct search experiments we obtain a 95% u
pper bound M-H < 335 GeV, (C) 2000 Elsevier Science B.V. All rights reserve
d.