Abstract Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 10 4 to 10 5 years . In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4 × 10 6 years . In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU . On the other hand, the number of escaped Hildas reaching the inner Solar System ( q < 2.5 AU ) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker–Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.