Comparison between results of test-particle and N-body simulations for the orbital evolution of Local Group spirals. Upper panels: Orbital evolution of the centre of mass of MW (blue), M31(red), and M33(green) for a set of initial conditions. Continuous lines are for test-particle simulations with C = 1 and crosses are the results from the corresponding N-body simulations. Bottom panel: Time evolution of the M31-M33 separation as given by N-body simulations for five sets of initial conditions (corresponding to the five colours) with C = 1.0. The open circles are for simulations that used 10000 particles for each galaxy while crosses refer to simulations with 40000 particles for each galaxy.