We present high spatial resolution near–infrared broad–band JHK and Br \gamma 2.166 \mu m and H _ { 2 } 1–0 S ( 1 ) 2.121 \mu m emission line images of the circumnuclear star formation rings in the LINER/Seyfert 1 galaxy NGC 1097 and in the Seyfert 2 galaxy NGC 6574 . We investigate the morphology , extinction , and the star formation properties and history of the rings , by comparing the observed properties with an evolutionary population synthesis model . The clumpy morphology in both galaxies varies strongly with wavelength , due to a combination of extinction , emission from hot dust and red supergiants , and the age of the stellar populations in the rings . The near–infrared and radio morphologies are in general agreement , although there are differences in the detailed morphology . From the comparison of Br \gamma and H \alpha fluxes , we derive average extinctions toward the hot spots A _ { V } = 1.3 for NGC 1097 and A _ { V } = 2.1 for NGC 6574 . The observed H _ { 2 } /Br \gamma ratios indicate that in both rings the main excitation mechanism of the molecular gas is UV radiation from hot young stars , while shocks can contribute only in a few regions . The starburst rings in both galaxies exhibit small Br \gamma equivalent widths . Assuming a constant star formation rate with M _ { u } = 100 M _ { \odot } results in extremely long ages ( up to 1 Gyr ) , in disagreement with the morphology and the radio spectral index of the galaxies . This situation is only slightly remedied by a reduced upper mass cutoff ( M _ { u } = 30 M _ { \odot } ) . We prefer a model of an instantaneous burst of star formation with M _ { u } = 100 M _ { \odot } occurring \sim 6–7 Myr ago . Gaseous nuclear bars parallel to the stellar nuclear bar were detected in both galaxies , and we derive M \sim 100 M _ { \odot } for the mass of the excited nuclear H _ { 2 } emission . Finally , we briefly discuss the connection between the rings , bars and the fuelling of nuclear activity .