Three approaches are presented to treat anisotropic scattering in neutron transport. The approaches are based on the even-odd-parity flux formalism and yield three different second-order equations for the even-parity flux. The first one is based on the total elimination of the odd-parity flux of the second-order equation. In the other two approaches, anisotropic scattering contributions are homogenized and incorporated into the collision term. The numerical solutions of these equations are implemented in the CRONOS code for pressurized water reactor core calculations and are done with a finite element spatial approximation and the discrete ordinates methods (SN) for the angular variable. Numerical results are presented for critical problems (keff) in x-y geometry. Comparisons with the APOLL02 assembly code show the accuracy and the efficiency of the proposed algorithms.