A new approach to search for and measure the electric dipole moment (EDM) of the proton, deuteron and some other light nuclei is presented. The idea of the method is to store two ion beams, circulating with different velocities, in a storage ring with crossed electric and magnetic guiding fields. One beam is polarized and its EDM is measured using the so-called 'frozen spin' method. The second beam, which is unpolarized, is used as a co-magnetometer, sensitive to the radial component of the ring's magnetic field. The particle's magnetic dipole moment (MDM) couples to the radial magnetic field and mimics the EDM signal. Measuring the relative vertical orbit separation of the two beams, caused by the presence of the radial magnetic field, one can control the unwanted MDM spin precession. Examples of the parameters for EDM storage rings for protons and other species of ions are presented. The use of crossed electric and magnetic fields helps to reduce the size of the ring by a factor of 10-20. We show that the bending radius of such an EDM storage ring could be about 2-3 m. Finally, a new method of increasing the spin coherence time, the so-called 'spin wheel', is proposed and its applicability to the EDM search is discussed.