A large CO, HCN multi-transition survey of 30 Luminous Infrared Galaxies () 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, CO J=2–1, HCN J=1–0, 3–2, 4–3 observations, resulting from hours of JCMT, 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 () unless their excitation is accounted for, b) CO cooling of such gas in ULIRGs may be comparable to that of the CII line at , and c) low excitation of the {\it global} molecular gas reservoir remains possible in such systems. In such cases the expected low CO line luminosities for $\rm J+1\geq 4$ can lead to a strong bias against their detection from ULIRGs at high redshifts.

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