Observations of slow shocks in the Earth's magnetotail at the plasma sheet-lobe boundaries have been well documented. We restudy the magnetic field data of two slow shocks: one was observed from Geotail on January 17, 1994 at XGSE=-92 RE, and another was observed from ISEE-3 on February 2, 1983 at XGSE=-220 RE. In both cases, the slow shock layer was followed by an adjoining rotational discontinuity layer on the postshock side. Compound structures each composed of a slow shock layer and an adjoining rotational discontinuity layer have been recently observed in interplanetary space from Wind, Geotail and Imp-8. Because the two successive discontinuities are very close to each other, the compound structure looks like a new kind of MHD discontinuity. It may be called a double discontinuity. Since double discontinuities exist not only in interplanetary space but also in the magnetotail region, they could be a general MHD structure in space plasma. ¿ 1997 American Geophysical Union