We present high spatial resolution ( \sim 0 \aas@@fstack { \prime \prime } 6 ) near–infrared broad–band JHK images and Br \gamma 2.1661 \mu m and H _ { 2 } 1–0 S ( 1 ) 2.122 \mu m emission line images of the nuclear regions in the interacting starburst galaxies NGC 520 , NGC 1614 and NGC 7714 . The near–infrared emission line and radio morphologies are in general agreement , although there are differences in details . In NGC 1614 , we detect a nuclear double structure in Br \gamma , in agreement with the radio double structure . We derive average extinctions of A _ { K } = 0.41 and A _ { K } = 0.18 toward the nuclear regions of NGC 1614 and NGC 7714 , respectively . For NGC 520 , the extinction is much higher , A _ { K } = 1.2 – 1.6 . The observed H _ { 2 } /Br \gamma ratios indicate that the main excitation mechanism of the molecular gas is fluorescence by intense UV radiation from clusters of hot young stars , while shock excitation can be ruled out . The starburst regions in all galaxies exhibit small Br \gamma equivalent widths . Assuming a constant star formation model , even with a lowered upper mass cutoff of M _ { u } = 30 M _ { \odot } , results in rather old ages ( 10 – 40 Myr ) , in disagreement with the clumpy near–infrared morphologies . We prefer a model of an instantaneous burst of star formation with M _ { u } = 100 M _ { \odot } , occurring \sim 6–7 Myr ago , in agreement with previous determinations and with the detection of W–R features in NGC 1614 and NGC 7714 . Finally , we note a possible systematic difference in the amount of hot molecular gas between starburst and Seyfert galaxies .