Using the asymptotic-expansion technique, we compute the dominant
two-loop electroweak corrections, of O(G_F m_t2), to production and
decay via a pair of photons or gluons of the CP-odd Higgs boson A0 in a
two-Higgs-doublet model with low- to intermediate values of the
Higgs-boson masses and ratio tan(beta)=v_2/v_1 of the vacuum expectation
values. We also study the influence of a sequential heavy-fermion
generation. The appearance of three gamma_5 matrices in closed fermion
loops requires special care in the dimensional regularisation of
ultraviolet divergences. The finite renormalisation constant for the
pseudoscalar current effectively restoring the anticommutativity of the
gamma_5 matrix, familiar from perturbative quantum chromodynamics, is
found not to receive a correction in this order. We also revisit the
dominant two-loop electroweak correction to the H → gamma gamma decay
width in the standard model with a fourth fermion generation.
