Captain Picard, Counselor Troi, Chief Engineer La Forge, and Lt. Commander Data are on a runabout shuttlecraft, returning to the Enterprise from a conference. As they near the ship, they encounter pockets of temporal disruptions that have very peculiar effects and could be lethal if they pass through them. They modify their sensors to avoid these and when they near the Enterprise find it and a Romulan warbird frozen in time. The warbird has fired a disruptor at the Enterprise, while the Federation ship has initiated a power transfer to the warbird.
Data and La Forge modify a set of personal force fields to nullify the temporal effects, and they transport aboard the ships to try to investigate the situation. On the Enterprise, they find the crew has been transporting aboard Romulans from the warbird, and one, in sickbay, has fired upon Dr. Crusher with his disruptor. The Enterprise warp engine has suffered a warp breach which, under normal circumstances, would consume the Enterprise in seconds. Picard, suffering "temporal narcosis" from standing close to the core breach, forces the four to return. On the warbird, they find the crew attempting to evacuate the ship with the Enterprise 's help; its main reactor, using artificial quantum singularities is undergoing a power surge. Investigating the engine closely, they find the singularity appears odd and discolored unlike other ones. When Data scans it with a tricorder, time briefly moves forward on the ship (causing a cataclysmic core explosion), but then reverses back to its original point (restoring ships and crews). La Forge spots a Romulan who was not in the same place as before; the Romulan suddenly touches him, shocking them both. The shock is nearly lethal to La Forge, and they disconnect the shield to freeze him in time, hoping to care for him later, while they take the Romulan back to the runabout.
There, they find the Romulan is really a creature from trans-dimensional space. He admits he and a companion had tried to recover the singularity from the Romulans, as it really is an egg carrying their young. In the process of trying to remove the singularity, he had created the power surge, resulting in the Enterprise coming to the Warbird's aid. The creature soon fades away, returning to trans-dimensional space. Picard, Troi, and Data return to the Enterprise and position themselves around the ship, ready to use their scanners to reverse time a few seconds to perform key actions to prevent the pending disasters. As Data is about to initiate his scan, he is attacked by the Romulan's companion, but defeats him.
Picard and the others reverse time; though the rest of the crew is surprised, Picard gives the order to continue to evacuate the Romulan ship, including La Forge, and terminate the power transfer, while Troi successfully pushes Dr. Crusher out of the way of the Romulan blast; the Romulan states he was only firing at a trans-dimensional creature that had disguised herself as a Romulan and had not meant to harm Crusher. In Engineering, Data safely stops the breach. However, the warbird continues to go critical, and the power transfer from the Enterprise cannot be stopped. Picard remotely powers the runabout into the power transfer beam's path, disrupting it and allowing the Enterprise to move away, after safely recovering the warbird crew. Just as the warbird's engines go critical, the ship disappears, along with the remaining time abnormalities. As the Enterprise crew repair the ship, Picard promises to return the Romulans safely to their homeworld.
At the close, Data is trying to examine human perception of time.