We explore the relation between colour (measured from photometry) and specific star formation rate (derived from optical spectra obtained by the Sloan Digital Sky Survey Data Release 4) of over 6000 galaxies (Mr≤−20.5) in and around (<3 r200) low-redshift (z < 0.12) Abell clusters. Even though, as expected, most red sequence galaxies have little or no ongoing star formation, and most blue galaxies are currently forming stars, there are significant populations of red star-forming and blue passive galaxies. This paper examines various properties of galaxies belonging to the latter two categories, to understand why they deviate from the norm. These properties include morphological parameters, internal extinction, spectral features such as EW(Hδ) and the 4000 Å break, and metallicity. Our analysis shows that the blue passive galaxies have properties very similar to their star-forming counterparts, except that their large range in Hδ equivalent width indicates recent truncation of star formation. The red star-forming galaxies fall into two broad categories, one of them being massive galaxies in cluster cores dominated by an old stellar population, but with evidence of current star formation in the core (possibly linked with active galactic nuclei). For the remaining red star-forming galaxies, it is evident from spectral indices, stellar and gas-phase metallicities and mean stellar ages that their colours result from the predominance of a metal-rich stellar population. Only half of the red star-forming galaxies have extinction values consistent with a significant presence of dust. The implication of the properties of these star-forming galaxies on environmental studies, like that of the Butcher–Oemler effect, is discussed.