  Multitransition 12CO, 13CO and 492 GHz [CI] measurements of the late-type
spiral galaxies NGC 6946 and M 83 (NGC 5236) show pronounced molecular gas
concentrations in rapid solid-body rotation within a few hundred parsec from
both nuclei. Their 12CO, 13CO and [CI] relative intensities are nearly
identical. However, the very different [CII] intensities imply that the
physical conditions are not. The slow decrease of 12CO intensities with
increasing rotational level marks the presence of significant amounts of warm
and dense molecular gas in both galaxy centers. Detailed modelling indicates
that both galaxiy centers contain at least two distinct molecular components: a
warm and dense component with T(kin) = 30-60 K, n(H2) = 3000-10 000 cc, and a
more tenuous hotter component with T(kin) = 100-150 K, n(H2) < 1000 cc). Atomic
carbon column densities exceed CO column densities by a factor of about 1.5 in
NGC 6946 and about 4 in M 83. Unlike NGC 6946, M 83 contains a significant
amount of molecular hydrogen associated with ionized carbon rather than CO. The
centers of NGC 6946 and M 83 contain nearly identical total (atomic and
molecular) gas masses of about 3 x 10**7 M(sun). Despite their prominence, the
central gas concentrations in these galaxies represent only a few per cent of
the stellar mass in the same volume. The peak face-on gas mass density is much
higher in M 83 (120 M(sun)/pc**2) than in NGC 6946 (45 M(sun)/pc**2). The more
intense starburst in M 83 is associated with a more compact and somewhat hotter
PDR zone than the milder starburst in NGC 6946.
