Context : Aims : We study the physical properties and amount of molecular gas in the central regions of galaxies with active nuclei . Methods : Maps and measurements of the J =1–0 , J =2–1 , J =3–2 , J =4–3 { { } ^ { 12 } CO } , the J =1–0 , J =2–1 , and J =3–2 { { } ^ { 13 } CO } lines in the central arcminute squared of NGC 1068 , NGC 2146 , NGC 3079 , NGC 4826 , and NGC 7469 , as well as 492 GHz CI maps in three of these are used to model the molecular gas clouds in these galaxies . Results : Bright CO concentrations were detected and mapped in all five objects . In all cases , the observed lines could be fitted with two distinct gas components . The physical condition of the molecular gas is found to differ from galaxy to galaxy . Rather high kinetic temperatures of 125-150 K occur in NGC 2146 and NGC 3079 . Very high densities of 0.3 - 1.0 \times 10 ^ { 5 } { cm ^ { -3 } } occur in NGC 2146 , NGC 3079 , and NGC 7469 . The CO to { H _ { 2 } } conversion factor X is typically an order of magnitude less than the ‘ standard ’ value in the Solar Neighborhood . The molecular gas is constrained within radii between 0.9 and 1.5 kpc from the nuclei . Within these radii , { H _ { 2 } } masses are typically 1.2 - 2.5 \times 10 ^ { 8 } M _ { \odot } . The exception is the ( relatively nearby ) merger NGC 4826 with R =0.3 kpc , and M = 3 \times 10 ^ { 7 } M _ { \odot } . The { H _ { 2 } } mass is typically about one per cent of the dynamical mass in the same region . Conclusions :