The transition from the adiabatic (Sedov) phase of a spherically symmetric supernova remnant is studied numerically. The input physics is kept as simple as possible, but the interstellar magnetic field is included. It is shown that, for sufficiently large values of the explosion energy and ambient density, multiple shocks are formed. These shocks continue to be formed until the expansion velocity of the remnant falls below 108 km/s. The X-ray luminosity of the remnant is also calculated and it is found that the mean X-ray temperature does not correlate with the expansion velocity once radiative cooling becomes important.