We combine beam-matched (CO)-C-13, (CO)-C-12 J = 3 --> 2 and J = 2 -->
1 line data to infer the molecular gas excitation conditions in the c
entral 500 to 1600 pc diameters of a small sample of infrared-bright e
xternal galaxies: NGC 253, IC 342, M83, Maffei 2, and NGC 6946. We fin
d that the central 170 to 530 pc diameter regions have typical molecul
ar gas densities ranging from less than or similar to 10(4) cm-3 (in M
83) to greater than or similar to 10(5) cm-3 (in NGC 253) and that, ou
tside of these regions, the densities are likely to be less than or si
milar to 10(4) cm-3. The molecular clouds outside the inner 170-530 pc
are at least as warm as the molecular clouds in our Galaxy. Column de
nsities derived from integrated (CO)-C-13 line strengths and Halpha su
rface brightnesses suggest that the star formation rate is enhanced in
the central 170-530 pc diameters by an order of magnitude over that i
nferred for the outer star-forming disks in spiral galaxies. The total
luminosity of each sample galaxy over all CO rotational lines is appr
oximately 10(5)-10(6) L., which is within an order of magnitude of tha
t of the important cooling line of [C II] at 158 mum. Additional obser
vations of the J = 1 --> 0 lines of (CO)-O-18 and (CO)-C-13 Suggest th
at emission from the central kiloparsec of spiral galaxies may be opti
cally thick in the (CO)-C-13 J = 1 --> 0 line. If so, estimates of mol
ecular gas mass using (CO)-C-13 integrated line strengths could be too
low. The sum of the molecular line observations imply the existence o
f two molecular gas components: a low-density [n(H-2) less than or sim
ilar to 10(3)-10(4) cm-3] component and a warm (T(K) greater than or s
imilar to 50 K), high-density [n(H-2) greater than or similar to 10(4)
-10(5) cm-3] component. The warm, dense component is probably associat
ed with star formation.