NOVELTY - Recovering nutrients (I) during recovery of oleaginous compounds from a non-vascular photosynthetic organism, comprises: obtaining a non-vascular photosynthetic organism in an aqueous medium; subjecting the non-vascular photosynthetic organism to recover oleaginous compounds, where the process produces at least an aqueous phase and an organic phase; and treating the aqueous phase to recover nitrogen and phosphorus.    USE - The method is useful for recovering nutrients during recovery of oleaginous compounds from non-vascular photosynthetic organism (claimed) and to extract lipids, fats, terpenes, hydrocarbons or other oleaginous compositions.    ADVANTAGE - The method: is applicable to any biomass (e.g. vascular plants); utilizes less acid without decrease in yield; provides final product with low impurities; and provides recovery of phosphorus and nitrogen in unified process.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for obtaining (II) oleaginous composition and recycling nutrients from biomass, comprising: (a) obtaining a feedstock comprising the biomass and water; (b) heating the feedstock in a closed reaction vessel to a first temperature of 250-360 degrees C for 0-90 minutes; (c) cooling the feedstock of step (b) to a temperature between ambient temperature and 150 degrees C; (d) acidifying the cooled feedstock of step (c) to a pH of 3-6 to produce an acidified composition; (e) heating the acidified composition of step (d) to a second temperature of 40-150 degrees C for 0-45 minutes; (f) adding a volume of a solvent equal in volume to the water in the acidified composition to the acidified composition of step (e) to produce a solvent extraction composition, where the solvent is sparingly soluble in water, but oleaginous compounds are at least substantially soluble in the solvent; (g) heating the solvent extraction composition in closed reaction vessel to a third temperature of 60-150 degrees C for 15-45 minutes; (h) separating the solvent extraction composition into at least an organic phase and an aqueous phase; (i) removing the organic phase from the aqueous phase; (j) removing the solvent from the organic phase to obtain an oleaginous composition; (k) and treating the aqueous phase to recover the nitrogen and phosphorus.