  In the present thesis I discuss the hard spectator interaction amplitude in
$B\to\pi\pi$ at NLO i.e. at $\mathcal{O}(\alpha_s^2)$. This special part of the
amplitude, whose LO starts at $\mathcal{O}(\alpha_s)$, is defined in the
framework of QCD factorization. QCD factorization allows to separate the short-
and the long-distance physics in leading power in an expansion in $\lqcd/m_b$,
where the short-distance physics can be calculated in a perturbative expansion
in $\alpha_s$. Compared to other parts of the amplitude hard spectator
interactions are formally enhanced by the hard collinear scale $\sqrt{\lqcd
m_b}$, which occurs next to the $m_b$-scale and leads to an enhancement of
$\alpha_s$.
  From a technical point of view the main challenges of this calculation are
due to the fact that we have to deal with Feynman integrals that come with up
to five external legs and with three independent ratios of scales. These
Feynman integrals have to be expanded in powers of $\lqcd/m_b$. I will discuss
integration by parts identities to reduce the number of master integrals and
differential equations techniques to get their power expansions. A concrete
implementation of integration by parts identities in a computer algebra system
is given in the appendix.
  Finally I discuss numerical issues like scale dependence of the amplitudes
and branching ratios. It will turn out that the NLO contributions of the hard
spectator interactions are important but small enough for perturbation theory
to be valid
