Just like their respective mentors, Calamity and Beeper would engage in the classic "Hunter and Prey", in which Calamity would try numerous attempts to capture Beeper, but with no success. However, unlike their mentors, When they are not engaged in the "Hunter and Prey", they sometimes act as friends, since they grew up together.
Times where Calamity and Beeper are good friends.
- In the episode, Animaniacs!, as Buster tells Plucky about the steps of animation, Calamity and Beeper work together when they add color to the drawings. However, Beeper accidentally sprays paint in Calamity's face, causing the Coyote to get revenge on Beeper by spraying him.
- In the Career Oppor-Toon-ities episode segment, Falling to Pizzas, after Calamity fails to be one of ten customers to get a free slice of pizza, Beeper convinces his boss to give Calamity a free slice as well. The slice turns out to be a hot chili pizza, which causes Calamity to fly into the air like rocket, explode in mid-air, and fall down to Earth, cracking the asphalt as he hits. At the end of the cartoon, Beeper is seen driving the ambulance to take Calamity to the hospital.
- In the New Class Day episode segment, The Just-Us League of Supertoons, while in their Little Dasher and Keen Arrow costumes, it is shown that Beeper and Calamity are on the same team.
- In the third wraparound of New Class Day, while heading towards the Classic Comedy Team classroom, Calamity and Beeper are shown to dress like the famous comedic duo, Oliver Hardy and Stan Laurel, who were known as the best of friends.
- In the Love Disconnection double-length episode segment, My Dinner With Elmyra , Calamity and Beeper are seen sitting together in the same booth at Weenie Burger.
Times where Calamity beats Beeper
Of all the cartoons starring Calamity and Beeper, Beeper would more often than not, beat Calamity. The only episode where Calamity beats Beeper is in the Dating, Acme Acres Style episode segment, Love Stinks.
- Throughout most of the episode, Beeper had Calamity beat as the latter was chased by Fifi. After Beeper scares Calamity and makes fun of him, he falls into the pit of leftover tar that Calamity got rid of, Calamity sees this as an opportunity to finally beat Beeper. Calamity gets the attention of a heartbroken Fifi, who sees Beeper as a skunk and begins chasing him, the same way she chased Calamity throughout the cartoon. As this happens, Calamity dances at having coming on top for once over his rival.