(abridged) We introduce and discuss the properties of a theoretical (B-K)-(J-K) integrated colour diagram for single-age, single-metallicity stellar populations. This combination of integrated colours is able to largely disentangle the well known age-metallicity degeneracy when the age of the population is greater than ~300 Myr. We discuss in detail the effect on this colour-colour diagram of alpha-enhanced metal abundance ratios, the presence of blue horizontal branch stars unaccounted for in the theoretical calibration, and of statistical colour fluctuations in low mass stellar systems. In the case of populations with multiple stellar generations, the luminosity-weighted mean age obtained from this diagram is shown to be heavily biased towards the youngest stellar components. We apply this method to several datasets for which optical and near-IR photometry are available in the literature. For the two Local Group dwarf galaxies NGC185 and NGC6822, the mean ages derived from the integrated colours are consistent with the star formation histories inferred independently from photometric observations of their resolved stellar populations. A sample of bright field and Virgo cluster elliptical galaxies is found to exhibit a range of luminosity-weighted mean ages from 3 to 14 Gyr, with a mean of 8 Gyr, independent of environment, and mean metallicities at or just above the solar value. Colour gradients are found in all of the galaxies studied, in the sense that central regions are redder. Aperture data for five Virgo early-type dwarf galaxies show that these galaxies appear to be shifted to lower mean metallicities and lower mean ages (range 1 to 6 Gyr) than their higher luminosity counterparts.
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