Axe Cop Saturdays, 11 p.m. (premieres July 21, 9:30 p.m.), Fox.

Blast Vegas Saturdays, 11:15 p.m. (premieres July 21, 9:45 p.m.), Fox.

The last time Fox attempted to counter-program Saturday Night Live, the result was the long-running but little-loved Mad TV, which ended in 2009. This week, the network launches a new late-night Saturday initiative it has branded Animation Domination High-Def. Although the new programming block will be going up against SNL, its format and style suggest that its real competition is Adult Swim, whose short, often nonsensical animated shows have built a large audience of teenagers and college students.

ADHD’s first two 15-minute shows, Axe Cop and High School USA!, are premiering in Sunday-night prime time before taking up their regular Saturday slots. Axe Cop is based on the comic book created by artist Ethan Nicolle from stories told by his 6-year-old brother Malachai. The show retains the weird logic and relentless energy of stories told by small children, with a kind of bizarre, twisted creativity. Anyone who’s ever listened to a 6-year-old tell a made-up story will recognize the way that Axe Cop jumps haphazardly from one moment to the next, explaining away inconsistencies with new inconsistencies.

Axe Cop’s talented voice cast is led by Nick Offerman as the title character (who is, of course, a cop with an axe), and there’s something inherently funny about hearing these accomplished performers deliver dialogue at least partially devised by a child. Of course, anyone who’s ever listened to a 6-year-old tell a made-up story also knows how quickly those stories become tedious and incoherent, and the biggest problem with Axe Cop is that once its stylistic novelty has worn off, it’s kind of annoying.

High School USA! is a more familiar Adult Swim-style show, created by Dino Stamatopoulos of Adult Swim’s Moral Orel and Mary Shelley’s Frankenhole. It’s a parody of high school dramas, with characters who look like they stepped out of a twisted version of Archie Comics. High school is a pretty tired target for mockery, and the first episode, which presents bullies as a misunderstood minority, doesn’t exactly feature sharp satire. Stamatopoulos explores some pretty dark material in the later episodes of Moral Orel, and High School USA! has the potential to go down that road as well. At the start, however, it’s mostly underwhelming compared to the sheer weirdness of Axe Cop. But both shows emulate the Adult Swim formula well, which means that they might succeed in bringing some of their target audience back to Fox.