There were no victims in either incident.
In the town of Karabulak, an improvised device exploded as a train carrying oil cisterns rolled past.
Russian media reported that bomb-disposal experts dispatched to the scene of the blast found a second unexploded device.
A second blast occurred a few hours later in a suburb of Nazran, the main city in Ingushetia. The explosion destroyed a mobile-phone base station, wrecked a small gas pipeline, and ignited a fire.