Invasive predators pose a substantial threat to global biodiversity. Native prey species frequently exhibit naïveté to the cues of invasive predators, and this phenomenon may contribute to the disproportionate impact of invasive predators on prey populations. However, not all species exhibit naïveté, which has led to the generation of many hypotheses to explain patterns in prey responses. These hypotheses primarily fall into two categories: system-centric hypotheses that relate to biogeographic isolation (BIH) and species-centric hypotheses, like the Archetype Similarity Hypothesis (ASH). We tested the predictions of these hypotheses by assessing the response of the common raccoon (Procyon lotor) and hispid cotton rat (Sigmodon hispidus), two native mammal species with divergent snake predation histories, to the cues of the invasive Burmese python (Python bivittatus) in Florida. Using giving-up densities (GUDs), we assessed the responses of both cotton rats and raccoons to life-size replicas of Burmese pythons and two North American predators (coyotes, Canis latrans, and eastern diamondback rattlesnake, Crotalus adamanteus). This Relative.GUD.Racoon dataset presents the results of giving-up density experiments conducted to assess raccoon responses to the visual cues of invasive Burmese pythons. Experiments were conducted in Paynes Prairie State Preserve Park (Alachua County, Florida, USA) in 2022. To quantify raccoon giving-up densities, we mixed 100 pieces of cat food with 1 liter of pine pellets. To minimize the influence of environmental variables on the treatments, we employed a blocked design, ensuring that each of the four predator treatments was represented in each cluster. This Relative.GUD.Rat dataset presents the results of giving-up density experiments conducted to assess hispid cotton rat responses to the visual cues of invasive Burmese pythons. Experiments were conducted in Paynes Prairie State Preserve Park (Alachua County, Florida, USA) in 2022. To quantify cotton rat giving-up densities, we mixed 25 ml of hulled millet with 1.5 liters of sifted sand. To minimize the influence of environmental variables on the treatments, we employed a blocked design, ensuring that each of the four predator treatments was represented in each cluster. We repeated treatments for three nights.