Experimental studies of the magnetoelectric effect in the antiferromagnetic crystals Cr20 3, Gd2CuO4 and Sm2CuO 4 have been performed in strong magnetic fields up to 20 T. The magnetoelectric effect is fully determined by the symmetry of the magnetically ordered material and yields hence valuable information about magnetic ground states. When the magnetic symmetry is changed at a magnetic field induced phase transition the magnetoelectric effect exhibits anomalies at the phase transition owing to the fact that the magnetoelectric signal is related to the antiferromagnetic order parameter L. Even at temperatures close to the Nrel temperature TN the obtained experimental data resolve the magnetic properties very well, giving the possibility to study magnetic phase transitions in the critical temperature range.