We present broadband (U, V, I, and H) and narrowband (H α+[N II] and Pa α) images of the circumnuclear starburst rings in two nearby spiral galaxies, NGC 1512 and NGC 5248, obtained with the WFPC2 and NICMOS cameras on HST. Combined with previously published ultraviolet (UV) HST images at 2300 Å, these data provide a particularly wide wavelength range with which to study the properties of the stellar populations, the gas, and the dust in the rings. The young star clusters and the line-emitting gas have different spatial distributions, with some large (50 pc scale) line-emitting regions that have little associated continuum emission, but a Pa α equivalent width indicating an embedded stellar population a few megayears old. The observed H α/Pa α intensity ratios suggest the gas is mixed with dust, making it effective at completely obscuring some of the young clusters. We identify the major (about 500 in each galaxy) compact continuum sources (super star clusters and individual stars) and analyze their spectral energy distributions (SEDs) from 0.2 to 1.6 μ m by fitting them with a grid of spectral synthesis models with a range of ages and dust extinction. Most of the visible clusters are only mildly reddened, with A V= 0 to 1 mag, suggesting that the processes that clear out the gas and dust of the stellar birth clouds are efficient and fast. The patchiness of the dust distribution makes it difficult to reliably estimate the star formation rate, based on UV continuum slope or hydrogen emission-line ratios, in starbursts such as these. The cluster SEDs are consistent with a range in ages, from 1 to 300 Myr, but with only a minority older than a few tens of megayears. We point out an age bias, the result of the steep luminosity function of the clusters combined with the fading of clusters as they age, which causes young clusters to be overrepresented at any luminosity. Accounting for this bias, the fraction of old clusters is consistent with continuous star formation in the rings over the past∼ 300 Myr. Because of the uncertainties in dating the clusters, we cannot rule out episodic,∼ 20 Myr long bursts of star formation, but the presence of UV-bright rings in about 10% of spiral galaxies argues against this possibility. Although most of the observed SEDs are well fitted by a range of models, some of the brightest young clusters have excess emission in the IR that is not predicted by the models and may be thermal reradiation by circumstellar dust. The cluster mass functions follow a power-law distribution with index-2, similar to that recently derived for the starburst in the merging Antennae galaxies, and extending to∼ 10 5 M⊙. The lack of a mass scale means that subsequent evolution of the mass function is required, if some of the SSCs are to evolve into globular clusters. The clusters are spatially unresolved or marginally resolved, corresponding to V-band Gaussian radii of less than a few parsecs, at an assumed distance of 10 Mpc. In NGC 5248, we report a previously unknown, 60 pc radius, inner emission-line ring, and in NGC 1512, a peculiar compact (0 &farcs; 1 diameter) source with an H α+[N II] equivalent width of∼ 7000 Å, which may be a so-called Balmer-dominated supernova remnant.