Context. The formation and evolution of dwarf galaxies is relatively difficult to understand because of their faint emission in all regimes that require large aperture telescopes. Aims: We intend to study the evolution of star-forming dwarf galaxies in clusters. We selected Fornax and Hydra clusters to complement our previous study of Virgo. On the basis of available literature data, we selected ten star-forming candidates in Fornax and another ten objects in Hydra. Methods: We used Gemini South with GMOS to acquire Hα images necessary to detect star-forming regions in the two galaxy samples. We then performed long-slit spectroscopy for the brightest six candidates, to derive their chemical properties. Finally, we employed the VLT with HAWK-I to observe all galaxies in the K' band to derive their main physical properties. Results: We studied the morphology of our two samples, finding five objects in Fornax and six in Hydra with structures consistent with those of star-forming dwarfs, i.e., dwarf irregulars (dIs) or blue compact dwarfs (BCDs). About four other objects are probably dwarf spirals, while three objects remained undetected in both visible and near infrared. On the basis of visible bright emission lines, we derived oxygen abundances for ten star-forming candidates with values between 8.00 ≤ 12+log(O/H) ≤8.78. Conclusions: Most fundamental properties of star-forming galaxies in Fornax and Hydra appear similar to corresponding properties of dIs and BCDs from Virgo and the local volume (LV). The luminosity-metallicity and metallicity-gas fraction relations in the LV and Virgo appear to be followed by Fornax and Hydra samples, suggesting that the chemical evolution of the two clusters seems consistent with the predictions from the closed box model, although larger samples are needed to investigate the role of possible environmental effects. Star-forming dwarfs (dIs and BCDs) in different environments appear to follow different mass-metallicity relations, with more metal-rich objects tending to occupy regions of higher galaxy overdensity in the Virgo and Hydra clusters. Treated separatelly, dIs and BCDs also appear to define different mass-metallicity relations, with BCDs following a steeper relation than dIs fitted alone. Only two objects from Fornax and Hydra appear confined to the dwarf fundamental plane (FP) which does not seem to hold for most Hydra objects, suggesting that the environment has some influence. A concerted effort is necessary to acquire deep radio data for these nearby clusters in conjunction with NIR imaging and spectroscopy. Based on observations acquired at Gemini South (GS-2007B-Q-53 and GS-2008A-Q-49) and ESO VLT (382.A-0409A).Full Figs. 1 and 2 are available in electronic form at http://www.aanda.org