Aqueous-organic or organic hydrogen peroxide solutions can be produced by direct synthesis in the presence of a catalyst fixed bed and an organic solvent. According to the invention, a non-explosive gas mixture comprising H₂ and O₂ is employed and a liquid reaction medium comprising organic solvent and bromide and/or iodide is passed over the fixed bed with a cross-section loading of at least 0.3 m/h. In the case of a trickle bed procedure with a cross-section loading of 0.3 m/h to 2 m/h, 4 to 10 wt. % methanolic H₂O₂ solutions can be prepared with a high productivity.