The Time Paradox Avoidance Enforcement Squadron also known as the Time Police is an organization from the future tasked with protecting the time stream from paradoxes, time-warps, and time anomalies.
The Squadron debuts in the episode "The Time Traveler's Pig," where agents Lolph and Dundgren are first seen. After learning that several time anomalies occurred, caused by Dipper and Mabel, Lolph and Dundgren were sent to retrieve Blendin Blandin, believing Blendin was responsible for the anomalies. They arrest Blendin at the Mystery Fair for violating the "Time Traveler's Code of Conduct." As they drag him away, Blendin claims Mabel and Dipper Pines were responsible, along with Waddles, their "leader," according to Blendin. The agents do not believe him and take him away, with Blendin swearing revenge against the twins.
Stan Pines then dares the agents to dunk him in the water, insulting their hair styles in the process. Lolph pulls out a laser arm cannon and fires at the target of the dunk tank, dunking Stan as he destroys the target. As everybody cheers at Stan's humiliation, they travel back to the future. They are then present as the Time Baby orders Blendin to clean up all the anomalies.
The pair makes another appearance in "Blendin's Game." Where the duo agents Lolph and Dungren open up a dimension just as Mabel and Dipper attempt to run onto the laser tag battle field. They announce a summons for the twins to fight in a battle arena dubbed "Globnar," they are being challenged by Blendin. He wishes to put Dipper and Mabel's lives on the line in an attempt to make them pay for wronging him in the past. As the episode progresses Mabel and Dipper attempt to break free, leading Lolph to believe Mabel was his grandmother from very far in the past to which his softer side is revealed leaving him vulnerable to Dipper stealing his Tape measure time and flee. Eventually after traveling too far back in time and coming up with a new plan, the Pines twins agree to battle Blendin.
In "Weirdmageddon Part 1," Blendin brings reinforcements from the Time Paradox Avoidance Enforcement Squadron, who send hologram projections to arrest Bill. However, Bill vaporizes the Time Baby and almost the whole time squadron, leaving only Blendin. 
In "Gravity Falls: Journal 3," it was revealed that Blendin is not the only survivor of Weirdmageddon. It was revealed that Lolph, Dundgren, and the other members send out holograms during such dangerous missions. They were not happy with Blendin's deal with Bill, leading up to said event. Because of this, they consider Blendin rogue because of this.
- 109. "The Time Traveler's Pig"
- Lolph and Dundgren are a reference to the actor Dolph Lundgren. Swapping the first letters of Dolph Lundgren's name makes Lolph and Dundgren.
- The outfits Lolph and Dundgren wear are very similar to those worn by Andrew Scott/GR13, who was Lundgren's character in the movie Universal Soldier.
- Time Baby knows and loathes Bill Cipher.