{ H _ { 2 } } column densities towards CO clouds in the LMC and SMC are estimated from their far-infrared surface brightness and HI column density . The newly derived { H _ { 2 } } column densities imply N ( H _ { 2 } ) / I ( CO ) conversion factors ( in units of 10 ^ { 21 } mol cm ^ { -2 } ( { Kkms ^ { -1 } } ) ^ { -1 } ) X _ { LMC } = 1.3 \pm 0.2 and X _ { SMC } = 12 \pm 2 . LMC and SMC contain total ( warm ) { H _ { 2 } } masses of 1.0 \pm 0.3 \times 10 ^ { 8 } M _ { \odot } and 0.75 \pm 0.25 \times 10 ^ { 8 } M _ { \odot } respectively . Local { H _ { 2 } } /HI mass ratios similar to those in LMC and SMC are found in the magellanic irregulars NGC 55 , 1569 , 4214 , 4449 and 6822 and in the extragalactic HII region complexes NGC 604 , 595 and 5461 in M 33 and M 101 respectively . In these HII regions and in NGC 4449 , we find X = 1–2 ; in NGC 55 , 4214 and 6822 X = 3–6 again in units of 10 ^ { 21 } mol cm ^ { -2 } ( { Kkms ^ { -1 } } ) ^ { -1 } . The post-starburst galaxy NGC 1569 has a very high value similar to that of the SMC . The CO– { H _ { 2 } } conversion factor X is found to depend on both the ambient radiation field intensity per nucleon { \it \sigma _ { FIR } } / { \it N _ { H } } and metallicity [ O ] / [ H ] : log X \propto 0.9 \pm 0.1 log \frac { { \it \sigma _ { FIR } } } { { \it N _ { H } } } - 3.5 \pm 0.2 log \frac { [ O ] } { [ H ] } . Neglecting dependency on radiation field , a reasonable approximation is also provided by log X \propto -2.7 \pm 0.3 log \frac { [ O ] } { [ H ] } . Milky Way values are consistent with these relations . This result is interpreted as the consequence of selective photodissociation of CO subjected to high radiation field energy densities and poor ( self ) shielding in low-metallicity environments , and especially the preferential destruction of diffuse CO in ‘ interclump ’ gas . Although locally { H _ { 2 } } may be the dominant ISM-component , the average global { H _ { 2 } } /HI mass ratio is 0.2 \pm 0.04 and the average { H _ { 2 } } gas mass fraction is 0.12 \pm 0.02 . Magellanic irregulars have warm molecular gas fractions very similar to those of our Galaxy , whereas other global properties ( mass , luminosity , metallicity , CO luminosity ) are very different .