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Multitransition 12CO, 13CO and 492 GHz [CI] measurements of the late-typespiral galaxies NGC 6946 and M 83 (NGC 5236) show pronounced molecular gasconcentrations in rapid solid-body rotation within a few hundred parsec fromboth nuclei. Their 12CO, 13CO and [CI] relative intensities are nearlyidentical. However, the very different [CII] intensities imply that thephysical conditions are not. The slow decrease of 12CO intensities withincreasing rotational level marks the presence of significant amounts of warmand dense molecular gas in both galaxy centers. Detailed modelling indicatesthat both galaxiy centers contain at least two distinct molecular components: awarm and dense component with T(kin) = 30-60 K, n(H2) = 3000-10 000 cc, and amore tenuous hotter component with T(kin) = 100-150 K, n(H2) < 1000 cc). Atomiccarbon column densities exceed CO column densities by a factor of about 1.5 inNGC 6946 and about 4 in M 83. Unlike NGC 6946, M 83 contains a significantamount of molecular hydrogen associated with ionized carbon rather than CO. Thecenters of NGC 6946 and M 83 contain nearly identical total (atomic andmolecular) gas masses of about 3 x 10**7 M(sun). Despite their prominence, thecentral gas concentrations in these galaxies represent only a few per cent ofthe stellar mass in the same volume. The peak face-on gas mass density is muchhigher in M 83 (120 M(sun)/pc**2) than in NGC 6946 (45 M(sun)/pc**2). The moreintense starburst in M 83 is associated with a more compact and somewhat hotterPDR zone than the milder starburst in NGC 6946.Comment: 12 pages; accepted for publication in A&

CI and CO in the spiral galaxies NGC 6946 and M 83