The paper analyzes strain localization in ductile single crystals undergoing single slip. It shows that strain localization, viewed as a bifurcation from a homogeneous deformation mode to a narrow shear band, occurs only when the plastic hardening modulus for the slip system reaches a critical value, $ h_{cr} $. This critical value depends on constitutive parameters that deviate from the Schmid rule of critical resolved shear stress. The study suggests that micromechanical processes like cross-slip can influence plastic response and are associated with localization. The paper develops a constitutive model for single slip, incorporating non-Schmid effects, and estimates the magnitude of parameters involved. It supports the notion that localization can occur with positive strain hardening, $ h_{cr} > 0 $, and that the often-invoked notions of ideally plastic or strain-softening states may be unnecessary. The paper also discusses the conditions for localization, showing that it occurs when the critical hardening rate is met, and that the orientation of the localization plane depends on the material's properties. The analysis includes the effects of small departures from the Schmid rule and the influence of cross-slip on the localization process. The results are derived using a dislocation model and are consistent with experimental observations of localization in ductile materials.The paper analyzes strain localization in ductile single crystals undergoing single slip. It shows that strain localization, viewed as a bifurcation from a homogeneous deformation mode to a narrow shear band, occurs only when the plastic hardening modulus for the slip system reaches a critical value, $ h_{cr} $. This critical value depends on constitutive parameters that deviate from the Schmid rule of critical resolved shear stress. The study suggests that micromechanical processes like cross-slip can influence plastic response and are associated with localization. The paper develops a constitutive model for single slip, incorporating non-Schmid effects, and estimates the magnitude of parameters involved. It supports the notion that localization can occur with positive strain hardening, $ h_{cr} > 0 $, and that the often-invoked notions of ideally plastic or strain-softening states may be unnecessary. The paper also discusses the conditions for localization, showing that it occurs when the critical hardening rate is met, and that the orientation of the localization plane depends on the material's properties. The analysis includes the effects of small departures from the Schmid rule and the influence of cross-slip on the localization process. The results are derived using a dislocation model and are consistent with experimental observations of localization in ductile materials.