QUARTIC MASS CORRECTIONS TO R(HAD)

The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the Z decay rate is calculated. The corrections are expanded in m(2)/s and alpha(s). Methods similar to those applied for the quadratic mass terms allow us to derive the c orrections of order alpha(s)m(4)/s(2) and alpha(s)(2)m(4)/s(2). Coeffi cients which depend logarithmically on m(2)/s and which cannot be abso rbed in a running quark mass arise in order alpha(s)(2). The implicati ons of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the b ottom threshold and for energies several GeV above the b (b) over bar threshold are discussed.