  In this paper we consider possible mechanisms to generate small Majorana
neutrino masses for active neutrinos in the scenario of gauge-Higgs
unification, a candidate for physics beyond the standard model. We stress that
it is non-trivial to find a gauge-invariant operator, responsible for the
Majorana masses, which is the counterpart of the well-known SU(2)$_L \times$
U(1)$_Y$ invariant higher-mass-dimensional ($d = 5$) operator. As the first
possibility we discuss the seesaw mechanism by assigning leptonic fields to the
adjoint representation of the gauge group, so that a $d = 5$ gauge-invariant
operator can be formed. It turns out that the mechanism leading to the small
Majorana masses is the admixture of the Type I and Type III seesaw mechanisms.
As the second possibility, we consider the case where the relevant operator has
$d = 7$, by introducing a matter scalar belonging to the fundamental
representation of the gauge group. Reflecting the fact that the mass dimension
of the operator is higher than usually expected, the Majorana masses are
generated by a "double seesaw mechanism."
