  We calculate the O(alpha_s) corrections to the Z^0-penguin and electroweak
box diagrams relevant for non-leptonic Delta F = 1 decays with F = S, B. This
calculation provides the complete O(alpha_w alpha_s) and O(alpha_w alpha_s
sin^2 theta_w m_t^2) corrections (alpha_w = alpha/sin^2 theta_w) to the Wilson
coefficients of the electroweak penguin four quark operators relevant for
non-leptonic K- and B-decays. We argue that this is the dominant part of the
next-next-to-leading (NNLO) contributions to these coefficients. Our results
allow to reduce considerably the uncertainty due to the definition of the top
quark mass present in the existing NLO calculations of non-leptonic decays. The
NNLO corrections to the coefficient of the color singlet (V-A)x(V-A)
electroweak penguin operator Q_9 relevant for B-decays are generally moderate,
amount to a few percent for the choice m_t(mu_t = m_t) and depend only weakly
on the renormalization scheme. Larger NNLO corrections with substantial scheme
dependence are found for the coefficients of the remaining electroweak penguin
operators Q_7, Q_8 and Q_10. In particular, the strong scheme dependence of the
NNLO corrections to C_8 allows to reduce considerably the scheme dependence of
C_8 (Q_8)_2 relevant for the ratio epsilon'/epsilon.
