We have performed a study of the rate of recent star formation for a sample of nearby compact groups of galaxies which have been taken from the compilation of Hickson (1982). Our sample included nearly all the compact groups in the Northern Hemisphere presenting more than three galaxies with accordant redshift z <= 0.02. Imaging of these groups in narrow band H_alpha and its adjacent continuum as well as in broad band Johnson BVI filters has been obtained for the sample. This information has allowed us to study the `effective' merging status of the galaxies in these compact groups and to derive a realistic estimate of their star formation rate. In spite of the high compacity of the groups and of what might be expected from the presumably high frequency of interactions, we have found clear signs of strong interaction between two (or three) galaxies only in three of the groups. In these three cases galaxies will eventually end as massive merger remnants. The galaxies in the rest of the groups show no significant enhancement of their star formation rate. Our results favour the idea that compact groups cover a wide range of dynamical stages, wile only a fraction of those groups are found in the later stages of evolution.