We present photometric and spectroscopic observations of the members of three previously cataloged compact group (CG) candidatesat redshifts $z>0.3$. These confirm spectroscopic  redshifts compatiblewith being gravitationally bound structures  at redshifts 0.3112, 0.3848and 0.3643 respectively, and then they are the most distant  CGs known with  spectroscopic confirmation for all their members.  The morphological and spectroscopic properties of all their galaxies  indicate early types dominated by an old population of stars, with little star formation or nuclear activity. Most of the physical properties derived for the three groups are quite similar to the average properties of  CGs at lower redshifts. In particular, from the velocities and positions of the respective members of each CG, we estimate short dynamic times. These leave open the questions of identifying the mechanism for forming CGs continuously and the nature of the final stages of these structures.