Plakortides R–U, four new polyketide endoperoxides, have been isolated from the marine sponge Plakinastrella mamillaris. Their structures were elucidated on the basis of extensive NMR spectroscopic (1H and 13C, COSY, HSQC, HMBC, and ROESY) and MS analyses and by chemical methods. In addition, a new method for the unambiguous stereochemical elucidation of 3,6-disubstituted 1,2-dioxines, frequently isolated from Plakinidae sponges, is reported. Pharmacological analysis demonstrated that plakortide U is endowed with in vitro antiplasmodial activity against a chloroquine-resistant strain.