Atomic models of twinning and formation of <110>-reorientation bands in bcc-crystals via bcc→fcc→bcctransformations accompanied by a change in the reverse transformation system are proposed. It is shown that {112} deformation twins are formed in the course of these transformations, when the shears and directions of homogeneous deformation of the reverse transformation occur in the crystallographically equivalent directions, making 60° angles with the initial direction (during the forward transformation) and the Kurdyumov–Sachs relations are valid. A fulfillment of the Nishiyama–Wassermann orientation relationships or a change in the type such dependence in the course of the reverse transformations gives rise to reorientation of the crystal lattice of these microbands around the <110>-type directions by the angles 60° or (60 ± 5.23)°. An important feature of these models is a considerable contribution of homogeneous transformation deformation of the martensitic type into the value of plastic deformation of the twin.