Implicit methods for the calculation of unsteady flows require the solution of large, sparse non-symmetric systems of linear equations. The size of such systems makes their solution by direct methods impractical and consequently iterative techniques are often used. A popular class of such methods are those based upon the conjugate gradient method. In this paper we examine three such methods, CGS, restarted GMRES and restarted GMRESR and compare their convergence properties.The University