We summarize our results based on observations with the NIRI camera on the Gemini North telescope of three Hii galaxies (Mrk 36, UM 408 and UM 461), obtained to identify and determine the ages and masses of the elementary components (the star cluster population) of the starburst regions in compact Hii galaxies. Our preliminary results indicate that the masses of the stellar clusters in these galaxies range from ~104 to ~106 M⊙, with associated ages of a few Myr. The most massive star clusters fall in the so-called super star cluster category. The identification of these clusters suggests that the formation and evolution of massive star clusters is the dominant mode of star formation in these galaxies. Their spatial distribution and ages seem to indicate that star formation is simultaneous over these timescales in some of our objects. We also review our recent description of the spatial distribution of physical conditions in the Hii galaxy UM 408 using the GMOS integral-field unit on Gemini South. The spatial distribution of the oxygen abundance does not show any significant variation or gradient across the galaxy on scales of hundreds of parsecs, within our observational uncertainties, confirming that this compact Hii galaxy, like other previously studied dwarf irregular galaxies, is chemically homogeneous.