In the Standard Model, we compute the leading two loop corrections growing like the second power of the Higgs mass to all the precision observables in electroweak physics. These corrections can be described in terms of their contributions to the parameters epsilon1 (or to DELTApho, or to T) and epsilon3 (or S) and are easily calculable in terms of few ultraviolet convergent diagrams. Previous results by Van der Bij and Veltman are confirmed. The relatively most sensitive observable is the Z width. However, to obtain corrections of the order of the foreseen precision at the end of the LEP1 phase, a Higgs mass of about 4 TeV is required. In practice, this makes them totally negligible.
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