In Picard's absence, Riker commands the Enterprise and responds to a Romulan ship's distress call. Meanwhile, Picard, Troi, La Forge, and Data are traveling aboard a long-range shuttlecraft known as a runabout, on their way back to the Enterprise from a conference. Suddenly, everyone but Troi freezes in mid-conversation. Seconds later, things return to normal. Perplexed, she attempts to describe the experience to the others when she inexplicably becomes frozen in time herself for over three minutes. The starboard nacelle cuts out from fuel loss, and readings indicate it has been in continuous operation for over 47 days. Picard then notices all the fruit in a bowl has rotted and aged; when he moves to touch it, his hand begins rapidly growing, causing him to yell in pain and attract the attention of the others who were in another part of the shuttlecraft. Data then discovers they are traveling through a temporal disturbance wherein time is moving approximately fifty times faster than normal. Their vessel, he finds, is surrounded by several temporal anomalies, and inside each, time is moving at different rates relative to normal space-time. The navigation computer maps the fragments and they maneuver about them. Eventually the runabout crew locate the Enterprise only to find it face-to-face with a Romulan Warbird. Both ships are frozen in time, with the Warbird firing a disruptor beam at the Enterprise, whose shields are down. The Enterprise is also directing a beam towards the Warbird, but it isn't a phaser blast.
The four officers adapt their emergency transporter armbands to generate skintight bubbles which will shield them from the temporal effects. Picard, Data, and Troi then beam onto the Enterprise bridge, where everything and everyone around them is motionless in the midst of action. The crewman assigned to the helm is lying on the deck and his place has been taken by a Romulan. Also several consoles show damage as a result of overloads. Picard consults the tactical board and finds that security have been sent to the Transporter Room and Sickbay. In addition Data reports a power surge in Engineering. Picard sends Troi and Data to Sickbay and Engineering respectively while he goes to the transporter room. On entering the transporter room Picard finds three Romulans who have just been beamed aboard by Worf. Troi finds security outside Sickbay and enters. There she is shocked to find that Dr. Crusher has been shot by a Romulan. Troi then receives a message from Data requesting that she and the Captain join him in Engineering. No sooner has she left Sickbay than one of the 'frozen' Romulans starts to move.
Picard (experiencing temporal narcosis) draws a smiley face in the steam produced by a warp core breach
Picard and Troi join Data in Engineering, where Data has discovered that the source of a power surge is a warp core breach that is progressing at an infinitesimal rate. (He explains that although time appeared to be frozen based on observations of the crew, his observation of the much more energetic explosion indicates that time is merely moving very slowly.) Data estimates that the explosion will consume the Enterprise in just over nine hours. Suddenly, Picard experiences severe emotional changes: he draws a smiley face in the cloud escaping from the warp core and begins laughing uncontrollably, becoming dizzy, and panicking. Geordi immediately transports the three back to the runabout. There they determine that the captain experienced a form of temporal narcosis. Deciding that it is too dangerous to expose him to the effects of the distortion a second time, Geordi, Data and Troi decide to investigate the Warbird's engine room this time while Picard remains on the runabout.
Transporting over to the Warbird, the away team finds the Romulan crew frozen, just like the crew on the Enterprise. In the engine room Troi examines the readouts and discovers that the crew are in the middle of an evacuation alert. Also they were attempting to shut down a power transfer originating from the Enterprise. When La Forge reports that the readouts indicate total engine failure, Troi is incredulous. Her experiences on a Warbird (specifically, the sixth-season episode "Face of the Enemy") taught her that Romulans use an artificial quantum singularity as a power source which, once activated, cannot be shut down. They open an inspection hatch on the warp core and find a strange green vortex with various black spots. When Data scans it with his tricorder it causes a reaction. Suddenly the Romulan crew begins moving, time seems to have resumed. The away team watch as the crew go about trying to save their ship. As they watch another Romulan enters the engine room and spots the away team. Suddenly, time starts going backwards. The crew revert to the positions they were in before time resumed. Meanwhile, Picard watches from the runabout as the Enterprise in normal time explodes from the warp core breach, then seconds later, reforms as time goes in reverse before freezing again.
With the engine room crew now frozen again Geordi moves towards one of the consoles. However, he notices that there is now a Romulan standing near the console, where there wasn't anyone standing before Data scanned the core. The Romulan grabs Geordi, shocking them both. Geordi is badly injured so Troi releases his armband, thus exposing him to the time distortion, which causes him to be frozen in time like the crew. Data and Troi return to runabout with the Romulan, who it turns out isn't a Romulan at all. He appears to be from a race which are from outside our space-time continuum. The being explains that he was attempting to rescue a nest of his species' young, which they mistakenly placed in the Romulan core, causing the engine failure. The aliens had mistaken the artificial singularity for a natural one, a black hole, which they use as nests. However the presence of the nest interfered with the engines and drained the Warbird's power. When the power transfer from the Enterprise made contact with the nest, the ruptures in time were created. The alien also states that he had a companion that had taken Romulan form. Before Picard can learn anything else, the being phases out in a kaleidoscope effect and vanishes.
Based on what they have observed, Picard theorizes that if they reverse the scanning effect of their tricorder, they can cause time to go backwards, then forward. This would allow them to save the ship, as well as Dr. Crusher and Commander La Forge. Picard, Troi, and Data return to the Enterprise and position themselves in three areas to make themselves most useful. Picard is on the bridge of the Enterprise, to make command decisions and explain things to Riker. Troi is in Sickbay to save Dr. Crusher from being killed by a Romulan disruptor beam. Data is in Engineering to prevent the power transfer from being initiated. He adjusts his tricorder, causing the aperture to make time reverse itself to a point before the warp core breach occurred, then go forward again. As time travels in reverse, the female alien to whom the other alien alluded attacks Data resulting in both of them being rendered unconscious. This prevents Data from stopping the power transfer. Riker sees Picard on the bridge and is confused, but Picard says he will explain later, simply ordering Riker to continue evacuating the Warbird and to beam Commander La Forge from the Warbird directly to Sickbay. Counselor Troi is able to pull Dr. Crusher from the Romulan's line of fire and orders him to surrender. However the Romulan explains that he wasn't firing at the Doctor but at the female alien that had taken Romulan form.
With Dr. Crusher and Commander La Forge safe but a warp core breach still in progress, Data erects a containment field around the warp core to delay the breach. Once Riker explains that moving the Enterprise would tear the ship apart due to feedback from the power transfer, Picard realizes the only option is the runabout. Picard remotely moves the runabout into the power beam. As soon as the runabout enters the path of the beam it is destroyed, thus restoring the normal flow of time. However, it also causes the Warbird to disappear. Riker is still confused, and Picard says that "It's going to take a little time to explain." Picard's states in his log that the Warbird's crew was successfully evacuated and will be returned in Romulan space.
The last scene is between Data and Riker. Riker has come to give Data the updated duty roster, and finds him in the middle of an experiment. Data's recent experiences with time have led him to consider how humans perceive time. Data is testing the saying "A watched pot never boils" by boiling a kettle of water and timing it, both when he watches it closely and when he ignores it completely. When Data stipulates that he cannot observe time any differently than his internal chronometer, Riker advises him to turn it off, since people do not have internal chronometers. When Data says he will try it, Riker jokingly amends, "Just don't be late for your shift!" After Commander Riker leaves the room, Data turns and notices that the water is boiling.