H_α luminosities of a sample of galaxies in nearby compact groups are presented. Our purpose is to study the influence of the group environment on the star formation rates (SFRs) of the galaxies in the groups, provided that the H_α luminosity is a good tracer of the SFR of disc galaxies. Measuring the global L/L_B of the groups - including early-type galaxies - we find that the average value of the H_α emission is not significantly different from that measured for field galaxies, and that most of the groups that show the highest level of L/L_B, with respect to a set of synthetic groups built out of field galaxies, show tidal features in at least one of their members. Finally, we have explored the relationship between the ratio L/L_B and several relevant dynamical parameters of the groups (velocity dispersion, crossing time, radius and mass-to-luminosity ratio) and have found no clear correlation. This suggests that the exact dynamical state of a group does not appear to control the SFR of the group as a whole.