AbstractGuided by the dispersion, surface of dynamical theory, we easily obtain evidence of the fact that in asymmetrical surface reflections (Bragg case) of X-rays at a perfect crystal, the angular widths of the incident and reflected beams are different from the same widths in the symmetrical Bragg case. The beam with the smaller glancing angle to the surface is angularly expanded, the other one, contracted (though in cross section, the former is contracted and the latter, expanded). Consequently, if the incident glancing angle is the smaller one (striping incidence, Vreftection), the angular width of the reflected beam is smaller than in the symmetric case (S-reflection), and that of the reflected section out of the primary beam is greater, and vice versa (striping emergence, if-reflection). At striping incidence, a contraction occurs, whereas at striping emergence, expansion of the angular reflection range occurs. These facts offer a number of possibilities for applying asymmetrical reflections to the well-known technique of the two crystal diffractometer—the author proposes the term “diffractometer” instead of the widely used “spectrometer”—in the (nv, −n)-position. These possibilities extend the efficiency of the double diffractometer with multiple effects, and some of them are given below: (1) Realization of rocking curves of extremely small angular width in the (nv, −nR)-position, and consequently increased sensibility of that width to lattice distortions, (2) Use of the extremely small angular width (or more strictly, the sharp θ-λ-coordination) of the beam emerging from a first crystal. This is in V-reflection for scanning the intrinsic diffraction pattern of the second crystal used in S- or V-reflection [(nv, −ns) or (nv, −nv) -position], (3) Increased steepness of the sides of the rocking curves using (nv, −nR) or (nv, −ns)-positions which allows double diffractometric topography (Bond-Andrus, Bonse-Kappler) of increased angular resolving power. (4) Repeated ^-reflections (eventually within a single crystal provided with a suitable groove) leading to further angular contraction of the resulting reflected beam and therefore further increased angular resolving power [(nv, −nv, nR, −nR)- and (nv, −nv, +nS)-positions]. Here the tails of the rocking curve are also suppressed by multiple reflection (Bonse-Hart).