We present results from a survey of molecular hydrogen emission from a sample of Starburst and Seyfert galaxies carried out with the Infrared Space Observatory ( ISO ) . Pure rotational H _ { 2 } emission has been detected in a number of extragalactic objects and a variety of environments . A number of transitions from S ( 7 ) to S ( 0 ) are detected in both Starbursts and Seyferts . Using excitation diagrams we derive temperatures and masses of the “ warm ” molecular hydrogen . We find that the temperature of the “ warm ” gas is similar in Starbursts and Seyferts ( those Seyferts for which we have firm detections of the S ( 0 ) line ) with a value of around T \sim 150 K. This “ warm ” gas accounts for as much as 10 % of the total galactic mass ( as probed by CO molecular observations ) in Starbursts . The fraction of “ warm ” gas is overall higher in Seyferts , ranging between 2–35 % . We then investigate the origin of the warm H _ { 2 } emission . Comparison with published theoretical models and Galactic templates implies that although emission from photodissociation regions ( PDR ) alone could explain the emission from Starbursts and Seyferts , most likely a combination of PDR , shock emission and gas heated by X-rays ( mostly for the Seyferts ) is responsible for H _ { 2 } excitation in extragalactic environments . Finally , we find that although PAH and H _ { 2 } line emission correlate well in Starbursts and the large scale emission in AGN , H _ { 2 } emission is much stronger compared to PAH emission in cases where a “ pure ” AGN dominates the energy output .