  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 ($\rm n\geq 10^4 cm^{-3}$) 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 $\rm J+1\to J$ line luminosities for $\rm
J+1\geq 4$ can lead to a strong bias against their detection from ULIRGs at
high redshifts.
