  Two optically obscured Wolf-Rayet (WR) stars have been recently discovered by
means of their infrared (IR) circumstellar shells, which show signatures of
interaction with each other. Following the systematics of the WR star
catalogues, these stars obtain the names WR\,120bb and WR\,120bc. In this
paper, we present and analyse new near-IR, $J$, $H$, and $K$-band, spectra
using the Potsdam Wolf-Rayet (PoWR) model atmosphere code. For that purpose,
the atomic data base of the code has been extended in order to include all
significant lines in the near-IR bands.
  The spectra of both stars are classified as WN9h. As their spectra are very
similar the parameters that we obtained by the spectral analyses hardly differ.
Despite their late spectral subtype, we found relatively high stellar
temperatures of 63 kK. The wind composition is dominated by helium, while
hydrogen is depleted to 25 per cent by mass.
  Because of their location in the Scutum-Centaurus arm, WR\,120bb and
WR\,120bc appear highly reddened, $A_{K_{\rm s}} \approx 2$ mag. We adopt a
common distance of 5.8\,kpc to both stars, which complies with the typical
absolute $K$-band magnitude for the WN9h subtype of -6.5 mag, is consistent
with their observed extinction based on comparison with other massive stars in
the region, and allows for the possibility that their shells are interacting
with each other. This leads to luminosities of $\log(L/L_\odot) = 5.66$ and
5.54 for WR\,120bb and WR\,120bc, with large uncertainties due to the adopted
distance.
  The values of the luminosities of WR\,120bb and WR\,120bc imply that the
immediate precursors of both stars were red supergiants (RSG). This implies in
turn that the circumstellar shells associated with WR\,120bb and WR\,120bc were
formed by interaction between the WR wind and the dense material shed during
the preceding RSG phase.
