In this report, the Cascadic Multigrid method (CMG), viewed as a «one-way» multigrid method not involving pre-smoothing or restriction steps, is defined and tested in the case of a simple 2D advection-diffusion problem. Jacobi and Gauss-Seidel smoothers are employed. While the Cascadic Multigrid method is very effective for relatively small Reynolds numbers, the convergenc- e rate deteriorates when advection and diffusion approximately balance each other. However, for larger Reynolds numbers, the method improves somewhat and achieves a mesh-independent convergence rate. In the next step, we recommend that the CMG method should be designed and tested for boundary layers in conjunction with adaptive meshes and/or semi-coarsening.