ORFEUS far UV echelle spectra have been used to investigate HI, Hz and CO a
bsorption lines along the line of sight towards LH 10:3120 in the LMC, exte
nding the study presented by de Beer et al. (1998). While Hz absorption is
clearly visible, no CO absorption at LMC velocities is detected, but an upp
er limit of N(CO) less than or equal to 3.3 x 10(13) cm(-2) for the CO colu
mn density is derived for the C-X band near 1088 Angstrom. The detected Hz
absorption features were used to determine a limit for the H-2/CO ratio of
N(H-2)/N((CO)-C-12) greater than or equal to 2.0 X 10(5) for the LMC gas al
ong this individual line of sight. Generally, the fraction of gas in molecu
lar form in the LMC is low compared to interstellar gas in the Milky Way wi
th the same total gas quantity. We compare the absorption spectroscopy with
SEST CO emission line measurements. It is found that most of the CO emissi
on 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 molec
ular hydrogen in the diffuse LMC gas.