By a completely independent analytic calculation made in general covar
iant gauge we confirm the known result for the massless O(alpha(s)(3))
correction to R(had) and check explicitly its gauge independence. We
extend the calculations to include contributions due to a hypothetical
existence of a colour octet of (light) neutral fermions known also un
der the name of gluinos. In numerical form and for five active flavour
s we found (in MS scheme) that R(s) = 11/3[1 + alpha(s)/pi + (1.409 -
0.346ng)(alpha(s)/pi)(2) + (-12.805 - 3.006n((g) over tilde) - 0.0466n
((g) over tilde)(2))(alpha(s)/pi)(3)] where n((g) over tilde) is the n
umber of such colour octets. The gluino (alpha(s)(3)) contribution to
the Z-boson hadronic decay rate proves to be relatively small while it
is significant for tau-lepton semihadronic width.