A large CO, HCN multi-transition survey of 30 Luminous Infrared Galaxies ($rm L_{IR}>10^{11} L_{odot}$) is nearing completion with the James Clerk Maxwell Telescope (JCMT) on Mauna Kea (Hawaii), and the IRAM 30-meter telescope at Pico Veleta (Spain). The CO J=1--0, 2--1, 3--2, 4--3,6--5, $ ^{13}$CO J=2--1, HCN J=1--0, 3--2, 4--3 observations, resulting from $sim 250$ hours of JCMT, $sim 100$ hours of 30-m observing time and data from the literature constitute {it the largest extragalactic molecular line survey to date}, and can be used to address a wide range of issues and eventually allow the construction of reliable Spectral Line Energy Distributions (SLEDs) for the molecular gas in local starbursts. First results suggest that: a) HCN and HCO$^+$ J=1--0 line luminosities can be poor mass estimators of dense molecular gas ($rm ngeq 10^4 cm^{-3}$) unless their excitation is accounted for, b) CO cooling of such gas in ULIRGs may be comparable to that of the CII line at $rm 158 mu m$, and c) low excitation of the {it global} molecular gas reservoir remains possible in such systems. In such cases the expected low CO $rm J+1to J$ line luminosities for $rm J+1geq 4$ can lead to a strong bias against their detection from ULIRGs at high redshifts.
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