  Preliminary results from a sensitive survey of the CO J=1--0, 2--1,
  3--2, 4--3, 6--5, HCN J=1--0, 3--2, 4--3, and CI J=1--0 lines of a sample of
30 Ultraluminous Infrared Galaxies (ULIRGs) are presented. These reveal a
tandalizing picture of the physical conditions of the molecular gas in these
extraordinary galaxies ($\rm L_{FIR}>10^{12} L_{\odot}$), with a diffuse phase
dominating the low-J CO lines and a much denser and warmer phase dominating the
CO 4-3 and 6-5 and all the HCN lines. The CI J=1--0 emission was found to be a
robust tracer of their total molecular gas mass under a large range of physical
conditions, a potent alternative to the much weaker emission from the $
^{13}$CO isotopologue, and especially promising as an H$_2$ tracer for similar
objects at high redshifts.

Astrophysics