  ORFEUS far UV echelle spectra have been used to investigate HI, H_2 and CO
absorption lines along the line of sight towards LH 10:3120 in the LMC,
extending the study presented by de Boer et al. (1998). While H_2 absorption is
clearly visible, no CO absorption at LMC velocities is detected, but an upper
limit of N(CO) < 3.3 10^13 cm^-2 for the CO column density is derived for the
C-X band near 1088 A. The detected H_2 absorption features were used to
determine a limit for the H_2/CO ratio of N(H_2)/N(CO) > 2.0 10^5 for the LMC
gas along this individual line of sight. Generally, the fraction of gas in
molecular form in the LMC is low compared to interstellar gas in the Milky Way
with the same total gas quantity. We compare the absorption spectroscopy with
SEST CO emission line measurements. It is found that most of the CO emission
comes from gas behind LH 10:3120. We discuss our results in view of the
possible scenario, in which the low dust content limits the amount of molecular
hydrogen in the diffuse LMC gas.
