We have undertaken an imaging survey of low surface brightness dwarf galaxies in nearby groups with the main goal of studying the faint-end of the galaxy luminosity function at z $\sim 0$. Here we describe the results on the search for LSB dwarf galaxies in two compact groups: HCG44 and HCG68. Our study explores the surface brightness, sizes, magnitudes and colours of these candidate dwarf galaxies. The selection criteria were their central surface brightness, scale factors and diameters at the limiting isophote of 26 R mag$/"^{2}$. We estimate the faint end of the luminosity function of galaxies through Monte Carlo simulations. The observed magnitude distribution of the candidate dwarf galaxies in the groups (down to $M_{R} \sim - 13$) is compatible with a Schechter function with a slope $\alpha \sim -1.2$.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html