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We present a detailed analysis of high resolution observations of the threelowest CO transitions in two nearby active galaxies, NGC4569 and NGC4826. TheCO(1-0) and (2-1) lines were observed with the Plateau de Bure Interferometerand the CO(3-2) line with the Submillimeter Array. Combining these data allowsus to compare the emission in the three lines and to map the line ratios,R21=I_{CO(2-1)}/I_{CO(1-0)} and R32=I_{CO(3-2)}/I_{CO(1-0)} at a resolution of~2", i.e., a linear resolution of 160 pc for NGC4569 and 40 pc for NGC4826. Inboth galaxies the emission in the three lines is similarly distributedspatially and in velocity, and CO is less excited (R32<0.6) than in theGalactic Center or the centers of other active galaxies studied so far.According to a pseudo-LTE model the molecular gas in NGC4569 is cold and mainlyoptically thick in the CO(1-0) and (2-1) lines; less than 50% of the gas isoptically thin in the CO(3-2) line. LVG modeling suggests the presence of anelongated ring of cold and dense gas coinciding with the ILR of the stellarbar. More excited gas is resolved in the circumnuclear disk of NGC4826.According to our pseudo-LTE model this corresponds to warmer gas with a ~50% ofthe CO(3-2) emission being optically thin. LVG modeling indicates the presenceof a semicircular arc of dense and cold gas centered on the dynamical centerand ~70 pc in radius. The gas temperature increases and its density decreasestoward the center. A near side/far side asymmetry noticeable in the CO, R32 andPa-alpha maps suggests that opacity effects play a role. Examining published COmaps of nearby active galaxies we find similar asymmetries suggesting that thiscould be a common phenomenon in active galaxies. These mainly qualitativeresults open new perspectives for the study of active galaxies with the futureAtacama Large Millimeter/submillimeter Array.

High-resolution mapping of the physical conditions in two nearby active galaxies based on 12CO(1-0), (2-1) and (3-2) lines