Animated plots frequently involve natural enemies chasing or hunting each other.
Can be Road Runner vs. Coyote if we see them comically failing repeatedly to catch it.
- One story in the Warhammer 40,000 comic Deff Skwadron involves the Orks repeatedly failing to intercept a messenger squig. They breed a special hunting squig to take it down, but find that it won't come back once the messenger is caught. The story ends with the skwadron's boss repeating "Catch that squig!"
- Wolf and Hare from Nu, Pogodi!.
- Pwt and Crraw in Muse Magazine.
- Sid & Al's Incredible Toons stars Sid E. Mouse and Al E. Cat. The objective of many of the puzzles is to set up a Rube Goldberg Device that will help one of them kill or eat the other.
- Tom and Jerry: The cat, Tom, is always chasing or otherwise trying to thwart the mouse, Jerry. It rarely ends well for Tom.
- Looney Tunes and Merrie Melodies:
- Sylvester and Tweety. The former, a cat, really wants to eat the latter, a canary, but never succeeds.
- Wile E. Coyote and the Road Runner. Wile E. Coyote tries repeatedly and fails repeatedly to catch the Road Runner so he can feast on him.
- Affable doofus hunter Elmer Fudd and Bugs Bunny and/or Daffy Duck.
- Hanna-Barbera's Blast-Off Buzzard and intended prey, Crazylegs the Snake, followed this trope as well.
- DePatie-Freleng's "The Ant and the Aardvark."
- As mentioned in the description, the Trope Namer is Dastardly and Muttley in Their Flying Machines.
- The Blue Racer is about the eponymous Blue Racer chasing (and failing to catch) a Japanese beetle.