In Russia, the whole intricate business of transporting the inperial family by rail was handled by the Inspection of Imperial Trains that was a part of the Ministry of Court. The Inspectors and their deputies were railway engineers from "good families" (Baron Shernwall, Baron Taube etc.) and usually carried honorary court ranks.
Their job was by no means easy. Russian emperors had a habit of keeping their travel plans tightly guarded even from trusted officials almost tiil the last minute. The reason was the illusory protection of their privacy, rather than security considerations. As a result, the involved officials - who really needed to know! - recruited paid informants among palace servants, and every "suspicious" packaging activity was immediately reported to whom it might concern.
Imperial trains were drawn by special engines only on suburb lines aroun SPb - to Tsarskoye, Peterhof, Gatchina etc. During long distance journeys, regular exchangable engines were used because steam locomotives needed to be cleaned and otherwise serviced every few hundred kilometers.
While senior grand dukes usually used "extra trains" composed of one or two carriages, it was quite customary - as noted by Harald - to have a personal carriage hooked up to a regular train. It was not unusual for the younger grand dukes just to book one or two 1st class compartments, especially for an overnight trip to Moscow or Helsingfors.
