In this thesis we develop the theory and evaluate the use of reference orbits which are the numerical results of previous calculations, in contrast to the analytical formulae of conventional Encke-type methods. The new techniques are applicable to the large scale integrations of solar system evolution studies, where many commensurabilities in the mean motions exist. Chapter 1 reviews the work which has been done in solar system evolution studies and chapter 2 describes some techniques which use analytical reference orbits. Chapter 3 considers many points of difficulty which occur when we apply the Taylor-series method using recurrence relations to many-body problems. In chapter 4 we present a discussion of the commensurabilities in mean motion which are to be found in the solar system. In chapters 5 and 6 the use of analytical reference orbits is replaced by the use of previously calculated and numerically stored reference orbits and the relevant differential equations are derived. The latter of these two chapters presents the results of a pilot project where we applied the general equations to a simple problem whose analytical solution is known. Several difficulties must be overcome before the new method can be programmed for the computer and their solutions are given in chapter 7 which outlines the complete implementation. The results of applying the method to some solar system problems are given in chapter 8. Here a comparison is made with conventional methods. Finally in chapter 9, another use of numerical reference orbits is developed, this time in combination with predictor-corrector methods.