The Enemy Release Hypothesis is often used to explain the success of non-native species invasions. Growing evidence indicates that parasite or pathogen species richness increases over time in invasive non-native species; however, this increase should not directly translate into release from enemy pressure as infection intensity of parasites (number of parasites per host) has a more profound impact on host fitness. The changes in intensity of parasitic infections in invasive non-native species have not yet been thoroughly analysed in newly colonized areas. The goal of this study was to determine whether gastrointestinal parasite (nematode and trematode) infection intensity has increased with time since the populations of American mink (Neovison vison) were established and how host demographic parameters affect infection intensity. We tested the Enemy Release Hypothesis by substituting space for time, evaluating parasite abundance in American mink at six sites along a chronosequence of mink invasion history. Nematode and trematode abundance increased with time since mink introduction, from a few parasites on average per mink after 16 years, to 200-250 parasites per mink after 34 years. The rate of increase in parasite abundance varied among demographic groups of mink (sex and age). Both nematodes and trematodes were more abundant in males than in females, and in subadults than in adults. Higher nematode abundance negatively affected body condition of mink. Our results provide evidence that non-native species are released from enemy pressure only in the first phase of invasion, and that infection is modulated by host demographics and season. These results contribute to the evaluation of the long-term patterns of parasite accumulation in invasive non-native species after their colonization of new territories.