  We investigate the characteristics of two newly discovered short-period,
double-lined, massive binary systems, VFTS 450 (O9.7$\;$II--Ib$\,$+$\,$O7::)
and VFTS 652 (B1$\;$Ib$\,+\,$O9:$\;$III:). We perform model-atmosphere analyses
to characterise the photospheric properties of both members of each binary
(denoting the `primary' as the spectroscopically more conspicuous component).
Radial velocities and optical photometry are used to estimate the binary-system
parameters. We estimate $T_{\rm eff}=27$ kK, $\log{(g)}=2.9$ (cgs) for the VFTS
450 primary spectrum (34kK, 3.6: for the secondary spectrum); and $T_{\rm eff}
= 22$kK, $\log{(g)}=2.8$ for the VFTS 652 primary spectrum (35kK, 3.7: for the
secondary spectrum). Both primaries show surface nitrogen enrichments (of more
than 1 dex for VFTS 652), and probable moderate oxygen depletions relative to
reference LMC abundances. We determine orbital periods of 6.89d and 8.59d for
VFTS 450 and VFTS 652, respectively, and argue that the primaries must be close
to filling their Roche lobes. Supposing this to be the case, we estimate
component masses in the range $\sim$20--50M$_\odot$. The secondary spectra are
associated with the more massive components, suggesting that both systems are
high-mass analogues of classical Algol systems, undergoing case-A mass
transfer. Difficulties in reconciling the spectroscopic analyses with the
light-curves and with evolutionary considerations suggest that the secondary
spectra are contaminated by (or arise in) accretion disks.
