A new method of obtaining Bragg reflection phases in an x-ray diffraction experiment is presented. It combines the phase-sensitive principles of multiple-beam diffraction and x-ray standing waves, and allows direct phase measurements of many multiple reflections simultaneously using a Bragg-inclined oscillating-crystal geometry. A modified-two-beam intensity function is devised to extract the phase information in a way similar to the standing wave analyses. [S0031-9007(98)05790-1] PACS numbers: 42.25.Fx, 78.70.Ck X-ray diffraction and scattering techniques are used widely in structural studies of crystalline materials. These techniques provide real-space charge density information by probing its Fourier components, or structure factors, in reciprocal space. In a typical diffraction experiment, what one measures is the intensity of a scattered or diffracted beam, which is related only to the structure factor amplitude and not to its phase. This loss of phase information is the classic phase problem in diffraction physics and crystallography, and its solution remains the most difficult part of a crystal structure determination [1].To date, all practical methods leading to solutions of the phase problem in crystallography can be grouped into two categories. In the first category are various mathematical techniques, such as the direct methods [2,3]. These methods rely largely on the overdetermination in the intensity measurements of a great number of Bragg reflections and use a probability distribution of possible phases to solve a crystal structure. While very powerful for small molecule structures, application of these statistics-based mathematical methods to larger crystal structures remains to be difficult and is still an active area of research. In the second category of crystallographic methods are various chemical methods involving heavy-atom derivatives and replacements [4], using x-ray dispersion corrections in the heavy-atom scattering factor in either single-or multiple-wavelength anomalous diffraction [5]. With these chemical methods, a crystal structure is solved by the additional phase information provided by the heavy-atom substructure. In general, the chemistry-based techniques often require complex and time-consuming chemical treatments to bond heavy atoms in proteins and other biological systems.In recent years, there have been considerable efforts to find a physical solution to the phase problem, namely, to obtain the phases of the Fourier components directly from diffraction experiments. One promising physical solution is the multiple-beam Bragg diffraction [6-9], which is based on the interference among simultaneously excited Bragg reflections. The effect has been shown visible both for small molecule compounds [10,11] and for complex crystals such as quasicrystals [12] and proteins [13,14]. The conventional technique for performing such an experiment involves exciting one Bragg reflection H and then rotating the crystal around the scattering vector H to bring another reflection G into its diffr...