A study of the use of a multilevel (multigrid) technique for the solution of Poisson and Navier-Stokes equations was conducted. Solutions were obtained using Gauss-Seidel, line-by-line, and strongly implicit relaxation schemes for the Poisson equation and Gauss-Seidel and strongly implicit schemes for the Navier-Stokes equations. In all test problems substantial improvement in the rate of convergence was found when using a multilevel ( multigrid) technique to reduce the low wave number errors with a Gauss-Seidel relaxation method. The rate of convergence improves, but less dramatically, when using a strongly implicit relaxation scheme. This is attributed to the fact that the strongly implicit scheme is itself quite efficient in reducing low wave number errors. It was also found that benefits from the use of multilevel ( multigrid) techniques are greater when the flow being predicted has strong pressure-momentum coupling.