We present J =2–1 , J =3–2 , J =4–3 ^ { 12 } CO and 492 GHz [ CI ] maps as well as J =2–1 and J =3–2 ^ { 13 } CO measurements of the late type spiral galaxies NGC 6946 and M 83 ( NGC 5236 ) . Both galaxies contain a pronounced molecular gas concentration in rapid solid-body rotation within a few hundred parsec from their nucleus . NGC 6946 and M 83 have nearly identical relative intensities in the ^ { 12 } CO , ^ { 13 } CO and [ CI ] transitions , but very different [ CII ] intensities , illustrating the need for caution in interpreting CO observations alone . The slow decrease of velocity-integrated ^ { 12 } CO intensities with increasing rotational level implies the presence of significant amounts of warm and dense molecular gas in both galaxy centers . Detailed modelling of the observed line ratios indicates that the molecular medium in both galaxies consists of at least two separate components . These are a warm and dense component ( T _ { kin } = 30 – 60 K , n ( { H _ { 2 } } ) = 3000 - 10000 { cm ^ { -3 } } ) and a much more tenuous hot component ( T _ { kin } = 100 – 150 K , n ( { H _ { 2 } } ) \leq 1000 { cm ^ { -3 } } ) . Total 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 \times 10 ^ { 7 } M _ { \odot } . 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 _ { \odot } pc ^ { -2 } ) than in NGC 6946 ( 45 M _ { \odot } 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 .