developed recently by @Le2014nonlinear to the case of crystals containing curved dislocations. Provided the dislocation network is regular in the sense that nearby dislocations have nearly the same direction and orientation, we introduce a loop function whose level curves coincide with the dislocation lines. Taking an infinitesimal area perpendicular to the dislocation line at some point of the crystal, we express the densities of edge and screw dislocations at that point through the resultant Burgers vectors of dislocations whose lines cross this area at right angle. Such scalar densities contain not only the information about the number of dislocations, but also the information about the orientation and curvature of the dislocation lines. In case of dislocation motion we introduce the vector of normal velocity of dislocation line through the time derivative of the loop function. Following @Kroener92 and [@Berdichevsky06] we require that the free energy density of crystal depends only on the elastic strain tensor and on the above scalar densities of dislocations. Then we formulate a new variational principle of CDT according to which the placement, the plastic slip, and the loop function in the final state of equilibrium minimize the free energy functional among all admissible functions. We 