The alignment of railway tracks may be monitored using an accelerometer (36) mounted on a bogie (24) of a railway vehicle to detect lateral accelerations, and a displacement transducer (38) to monitor the lateral displacements of a wheelset (27) relative to the bogie. The acceleration signals are digitised, and processed corresponding to double integration, so as to deduce the lateral displacements of the bogie, and in conjunction with the signals from the displacement transducer hence to determine the effective lateral displacements of the track. This can provide a more useful indication of the lateral positions of the rails than measurements of the gauge faces. Such equipment (16) may be installed in a service vehicle, and operate automatically, downloading resulting data to a remote base station at regular intervals.