The growth of the Gordon-Haus timing jitter in dispersion-managed soliton communication systems without in-line control is measured. After 650 km transmission with an average dispersion of D-AVG = 0.87 ps/nm/km and a pulse width, T-FWHM = 14 ps, compatible with 20 Gbit/s, only 45 fs of timing jitter is measured. This indicates that medium-range dispersion-managed soliton transmission systems has, in general, a good margin towards Gordon-Haus timing jitter.