H &alpha luminosities are presented in order to study the Star Formation Rates (SFRs) of a sample of galaxies in compact groups from Hickson's (1982) catalogue. Although the comparison of the SFRs of the disk galaxies in our sample with those of a sample of field galaxies yielded no difference between the average SFRs for disk galaxies in compact groups and in the field, environmental effects seem to influence the H &alpha luminosities of late and early-type galaxies in compact groups. No relationship was found between the total normalized H &alpha luminosities of the groups and some dynamical parameters, indicating that the dynamical state of the group does not influence the SFR of the group. The lack of dominant interaction induced starbursts in our sample is compatible with a scenario for compact groups of galaxies in which the dark matter of the group is arranged in a common halo, thereby preventing a fast collapse of the galaxies.