An efficient method for the synthesis of new spiro-tetraoxadodecanediamines and tetraoxazaspirobicycloalkanes has been developed by reactions of primary arylamines with gem-dihydroperoxides and α,ω-dialdehydes (glyoxal, pentanedial) catalyzed by lanthanide catalysts. A potential pathway for formation of tetraoxaspirododecane-diamines and tetraoxazospirobicycloalkanes has been proposed that involves generation of intermediate tetraoxaspiroalkanediols under the reaction conditions. The structures of the crystalline products have been confirmed by XRD. It was shown that the synthesized tetraoxazaspirobicycloalkanes exhibit high cytotoxic activity against Jurkat, K562, and U937 tumor cultures and Fibroblasts.