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.
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