COVID-19 infection usually occurs in children in a mild form, but some of them in a delayed period (one or several weeks after acute infection with COVID-19) may develop a severe inflammatory disease with clinical manifestations similar to toxic shock syndrome (Kawasaki disease), classified as multisystem inflammatory syndrome in children (MISC). It is possible that the syndrome has only a temporary connection with the COVID-19 infection. In the future, new associations of such clinical manifestations with other infectious (or non-infectious) diseases may appear. But currently, all children in the described cohorts with MISC have an association with COVID-19 infection. It is believed that the syndrome is initiated by an excessive adaptive immune response with the formation of autoantibodies. Treatment is based on anti-inflammatory, including steroid therapy, the possible use of intravenous immunoglobulin, aspirin, interleukin 1 and 6 receptor antagonists. The article analyzes current views on Kawasaki-multisystem inflammatory syndrome in children in the delayed period of COVID-19 coronavirus infection in the aspects of diagnosis, pathogenesis, clinical manifestations (with a discussion of foreign and Russian studies) and approaches to therapy and possible prevention, including the possibility of using plasmapheresis in complex therapy.