  The complete two-loop correction to the quark propagator, consisting of the
spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the
noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had
already been computed.) The chief technical tools include the powerful matrix
integration technique, the n^*-prescription for the spurious poles of 1/qn, and
the detailed analysis of the boundary singularities in five- and
six-dimensional parameter space. It is shown that the total divergent
contribution to the two-loop correction Sigma_2 contains both covariant and
noncovariant components, and is a local function of the external momentum p,
even off the mass-shell, as all nonlocal divergent terms cancel exactly.
Consequently, both the quark mass and field renormalizations are local. The
structure of Sigma_2 implies a quark mass counterterm of the form $\delta m
(lcg) = m\tilde\alpha_s C_F(3+\tilde\alpha_sW) + {\rm O} (\tilde\alpha_s^3)$,
$\tilde\alpha_s = g^2\Gamma(\eps)(4\pi)^{\eps -2}$, with W depending only on
the dimensional regulator epsilon, and on the numbers of colors and flavors. It
turns out that \delta m(lcg) is identical to the mass counterterm in the
general linear covariant gauge. Our results are in agreement with the
Bassetto-Dalbosco-Soldati renormalization scheme.
