  Higher-order corrections to the MSSM Higgs-boson masses are desirable for
accurate predictions currently testable at the LHC. By comparing the prediction
with the measured value of the discovered Higgs signal, viable parameter
regions can be inferred. For an improved theory accuracy, we compute all
two-loop corrections involving the strong coupling for the Higgs-boson mass
spectrum of the MSSM with complex parameters. Apart from the dependence on the
strong coupling, these contributions depend on the weak coupling and Yukawa
couplings, leading to terms of $\mathcal{O}{\left(\alpha\alpha_s\right)}$ and
$\mathcal{O}{\left(\sqrt{\alpha_{q_1}}\sqrt{\alpha_{q_2}}\alpha_s\right)}$,
($q_{1,2}=t,b,c,s,u,d$). The full dependence on the external momentum and all
relevant mass scales is taken into account. The calculation is performed in the
Feynman-diagrammatic approach which is flexible in the choice of the employed
renormalization scheme. For the phenomenological results presented here, a
renormalization scheme consistent with higher-order corrections included in the
code $\texttt{FeynHiggs}$ is adopted. For the evaluation of the results, a
total of $513$ two-loop two-point integrals with up to five different mass
scales are computed fully numerically using the program $\texttt{SecDec}$. A
comparison with existing results in the limit of real parameters and/or
vanishing external momentum is carried out, and the impact on the lightest
Higgs-boson mass is discussed, including the dependence on complex phases. The
new results will be included in the public code $\texttt{FeynHiggs}$.
