set of kinematic equations is derived for the dislocation density and curvature that requires the knowledge about the dislocation velocity. The relation between the dislocation density and the macroscopic plastic slip rate via the dislocation velocity is postulated in form of Orowan’s equation. The couple system of crystal plasticity and continuum dislocation dynamics becomes closed by the constitutive equation of a flow rule type (see [@Hochrainer2014; @Sandfeld2011; @Sandfeld2015; @Wulfinghoff2015]). In addition to the heavy computational cost of such theory, the relation to thermodynamics of crystal plasticity and to the LEDS-hypothesis is completely lost: the equilibrium solution found in this theory may not minimize the energy of crystal among all admissible dislocation configurations. Let us mention also a continuum approach proposed recently by @Zhu2013 [@Zhu2014] in which the three-dimensional dislocation structure is characterized by two families of disregistry functions that may take only integer values. The dislocation density can then be expressed in their terms. The coupled system of equations is derived from the underlying discrete dislocation dynamics for the displacement and disregistry functions. This approach is subject to the same critics as that proposed in [@Hochrainer2007].

The aim of this paper is to extend the nonlinear continuum dislocation theory (CDT) 