  Using the asymptotic-expansion technique, we compute the dominant two-loop
electroweak corrections, of O(G_F m_t^2), to production and decay via a pair of
photons or gluons of the CP-odd Higgs boson A^0 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.
