  HD 93129A was classified as the earliest O-type star in the Galaxy (O2~If*)
and is considered as the prototype of its spectral class. However,
interferometry shows that this object is a binary system, while recent
observations even suggest a triple configuration. None of the previous spectral
analyses of this object accounted for its multiplicity. With new
high-resolution UV and optical spectra, we have the possibility to reanalyze
this key object, taking its binary nature into account for the first time. We
aim to derive the fundamental parameters and the evolutionary status of HD
93129A, identifying the contributions of both components to the composite
spectrum. We analyzed UV and optical observations acquired with the Hubble
Space Telescope and ESO's Very Large Telescope. A multiwavelength analysis of
the system was performed using the latest version of the Potsdam Wolf-Rayet
model atmosphere code. Despite the similar spectral types of the two
components, we are able to find signatures from each of the components in the
combined spectrum, which allows us to estimate the parameters of both stars. We
derive $\log (L/L_\odot) = 6.15$, $T_{\textrm{eff}}=52$ kK, and $\log
\dot{M}=-4.7 [M_\odot\text{yr}^{-1}]$ for the primary Aa, and $\log
(L/L_\odot)=5.58$, $T_{\textrm{eff}}=45$ kK, and $\log\dot{M}=-5.8
[M_\odot\text{yr}^{-1}]$ for the secondary Ab. Even when accounting for the
binary nature, the primary of HD 93129A is found to be one of the hottest and
most luminous O stars in our Galaxy. Based on the theoretical decomposition of
the spectra, we assign spectral types O2~If* and O3~III(f*) to components Aa
and Ab, respectively. While we achieve a good fit for a wide spectral range,
specific spectral features are not fully reproduced. The data are not
sufficient to identify contributions from a hypothetical third component in the
system.
