Methods of metallography, X-ray diffraction, transmission electron microscopy, and dilatometry have been used to study the formation of the structure of pseudo-single crystals of nitrogen-bearing steel Kh18AG20 upon the δ → γ (bcc → fcc) transformation, in pseudo-single crystals of pure cobalt and binary alloy Co-29.7% Ni upon the β → α (fcc → hcp) transformation, and in pseudo-single crystals of zirconium upon the β → α (bcc → hcp) transformation. It has been established that the precipitation of austenite from ferrite during the δ → γ transformation in a single crystal of the Kh18AG20 steel occurs via a crystallographically ordered mechanism with the fulfillment of orientation relationships close to the Kurdjumov-Sachs orientation relationships. In the volume of the pseudo-single crystal there were realized six orientations of austenite with the retention at room temperature of a significant fraction of residual δ (α) ferrite. It has been shown that in the process of cooling of the β single crystals of cobalt, Co-29.7% Ni alloy, and zirconium to below the temperature of the β → α transition there formed several crystallographic orientations of the α phase that are grouped into packets. In each packet, there exist crystals of the α phase of one orientation. In accordance with the Wassermann orientation relationships, in the pseudo-single crystals of cobalt and Co-29.7% Ni alloy there are realized packets of four variants. In the pseudo-single crystal of zirconium, six variants of packets based on the Burgers orientation relationships are realized.