We report on the detection of two Halpha-emitting extreme compact objects from deep images of the Abell 634 and Abell 539 clusters of galaxies at z ~ 0.03. Follow up long slit spectroscopy of these two unresolved sources revealed that they are members of their respective clusters showing HII type spectra. The luminosity and the extreme equivalent width of Halpha+[NII] measured for these sources, together with their very compact appearance, has raised the question about the origin of these intense starbursts in the cluster environment. We propose the compact starburst in Abell 539 resulted from the compression of the interstellar gas of a dwarf galaxy when entering the cluster core; while the starburst galaxy in Abell 634 is likely to be the result of a galaxy-galaxy interaction, illustrating the preprocessing of galaxies during their infall towards the central regions of clusters. The contribution of these compact star-forming dwarf galaxies to the star formation history of galaxy clusters is discussed, as well as a possible link with the recently discovered early-type ultra-compact dwarf galaxies. We note that these extreme objects will be rarely detected in normal magnitude-limited optical or NIR surveys, mainly due to their low stellar masses (of the order of 10^6 solar masses), whereas they will easily show up in dedicated Halpha surveys given the high equivalent width of their emission lines.