We present subarcsecond-resolution, ground-based, near-infrared images of the central regions of a sample of 12 barred galaxies with circumnuclear star formation activity, which is organized in ring-like regions typically 1 kpc in diameter. We also present Hubble Space Telescope near-infrared images of 10 of our sample galaxies, and compare them with our ground-based data. Although our sample galaxies were selected for the presence of circumnuclear star formation activity, our broad-band near-infrared images are heterogeneous, showing a substantial amount of small-scale structure in some galaxies, and practically none in others. We argue that, where it exists, this structure is caused by young stars, which also cause the characteristic bumps or changes in slope in the radial profiles of ellipticity, major axis position angle, surface brightness and colour at the radius of the circumnuclear ring in most of our sample galaxies. In seven out of 10 HST images, star formation in the nuclear ring is clearly visible as a large number of small emitting regions, organized into spiral arm fragments, which are accompanied by dust lanes. Near-infrared colour index maps show much more clearly the location of dust lanes and, in certain cases, regions of star formation than single broad-band images. Circumnuclear spiral structure thus outlined appears to be common in barred spiral galaxies with circumnuclear star formation.