The implementation of local preconditioning in the CFD code EURANUS [1] is briefly addressed. Several preconditioning methods have been taken into account, including those developed respectively by Turkel [2], Choi and Merkle [3] and by Hakimi [4]. The main motivation of using local preconditioning is to improve the computational performance of the compressible code based on time-marching techniques when applied to solving for low-speed compressible and incompressible flows. The implementation strategies are presented and discussed in association with the corresponding modifications resulted from the preconditioned equation system, such as the artificial dissipation and the boundary conditions. It is demonstrated through several application examples that all the implemented preconditioners show very promising performance to accelerate the convergence rate in computations of external inviscid and viscous flows. For incompressible internal flows, moreover, the use of local preconditioning exercises also rather encouraging performance as compared with solutions obtained from an incompressible code using pressure-based schemes. It is expected that this report can be used as a supplemental reference when local preconditioning is employed in computations using the EURANUS code.