The magnetic order, moments, and ordering temperatures for La1-tMnO3+delta depend strongly on its nonstoichiometry. Powder neutron diffraction samples were obtained via precursor based synthesis, annealing in atmospheres with controlled oxygen partial pressures, and adequate quenching or slow cooling. The samples are representative for most of the nonstoichiometric domain. Three modifications of La1-tMnO3+delta were studied. First, the reduced phase with Jahn-Teller deformed Mn-III is orthorhombic (ORT1) and orders antiferromagnetically (A(x) mode), typically T-N approximate to 140 K and mu(AF) approximate to 3.4 mu(B) (0.00 less than or equal to t less than or equal to 0.08). All samples of this type exhibit parasitic ferromagnetism. Second, the fully oxidized samples have average Mn oxidation state around 3.2, and have rhombohedral (RH) crystal structure with ferromagnetic order at low temperatures; T-c approximate to 213 +/- 10 K and mu(F) = 3.9 +/- 0.1 mu(B) for La0.96MnO3.05. Third, for intermediate oxygen contents an orthorhombic structure (ORT2) occurs, with minor distortions of the MnO6-octahedra. For LaMnO3.08 of ORT2-type, ferromagnetic order (F-y mode) occurs below T-c = 125 +/- 10 K. The ordered magnetic moment, mu(F) = 2.46 +/- 0.04 mu(B) is rather small, LaMnO3.15 also takes the ORT2-type structure at low temperature, as proved by weak super-structure reflections. At 200 +/- 20 K, LaMnO3.15 undergoes a first order transition to the RH-type. The ordered magnetic moment, if present, is very small and in any case far from expectations for Mn-III/Mn-IV mixtures. It is proposed that the approximately 3:1 ratio between Mn-III and Mn-IV atoms in LaMnO3.15 gives rise to a frustrated system with largely spin glass behaviour. (C) 1996 Academic Press, Inc.