We present a study of the optical spectra of a sample of eight star-forming nuclear rings and the nuclei of their host galaxies. The spectra were obtained with the Intermediate dispersion Spectrograph and Imaging System spectrograph on the William Herschel Telescope and cover a wide range in wavelength, enabling the measurement of several stellar absorption features and gas emission lines. We compared the strength of the absorption lines to a variety of population synthesis models for the star formation history in the nuclear rings, including also the contribution of the older bulge and disc stellar components. In agreement with our previous investigation of the nuclear ring of NGC 4321, which was based on a more restricted number of line-strength indices, we find that the stars in our sample of nuclear rings have most likely formed over a prolonged period of time characterized by episodic bursts of star formation activity. Constant star formation is firmly ruled out by the present data, whereas a one-off formation event is an unlikely explanation for a common galactic component such as nuclear rings. The nuclear rings of NGC 4314 and NGC 7217 have distinct line-strength properties that set them apart from the rest of our sample, which are due to a larger contribution of bulge star in the observed spectra and, in the case of NGC 4314, to a younger stellar population in the ring. We have used emission-line measurements to constrain the physical conditions of the ionized gas within the rings, using the ratio of the [SII]λλ6716, 6731 lines to estimate the density of the gas, and photoionization model grids within specific diagnostic diagrams to derive metallicity. We find that emission in all nuclear rings originates from HII regions with electron densities typical for these kinds of objects, and that the rings are characterized by values for the gas metallicity ranging from slightly below to just above solar. We have also studied the spectra of the nuclei of our sample galaxies, all of which display emission lines. Consistent with previous studies for the nuclear activity and stellar populations, the majority of our nuclei appear to be dominated by old stellar populations and by Low-Ionization Nuclear Emission Region like emission. As 20 per cent of nearby spiral galaxies host nuclear rings that are presently forming massive stars, our finding of an episodic star formation history in nuclear rings implies that a significant population remains to be identified of young nuclear rings that are not presently in a massive star formation phase. Nuclear rings may thus be a much more common galactic component than presently known.