The Hilda asteroid group and Jupiter Trojans (JTs) are populations of primitive minor bodies whose origins have not been conclusively determined. In the framework of the so-called Nice Model, they are icy bodies scattered from the Kuiper Belt in an early epoch of the Solar System (the Late Heavy Bombardment) and finally trapped in the stable regions in which they are located today, in 3:2 and 1:1 resonances with Jupiter. Comparing detailed compositional and physical studies of these populations can thus help constrain dynamical models and provide clues about several key aspects of planetary science. However, because their visible and near-infrared spectra are featureless, the diagnostic spectral information available is scarce and has been obtained in different wavelength ranges, e.g., 10-micron emission plateaus characteristic of fine-grained silicates detected on JTs [Emery et al. 2006. Icarus 182, 496E], or the 3-micron features detected on four Hildas: three of them associated with water ice, one related to hydrated silicates [Takir & Emery 2012. Icarus, 219 641T]. Studying the 3-micron region from ground-based facilities is complicated, particularly for these distant populations, and no such bands have been detected on JTs within the achieved signal-to-noise ratios. But if these objects share a common origin and similar evolution, they should show similar properties. Now, the space-based Wide-field Infrared Survey Explorer (WISE) has provided infrared data of hundreds of JTs and Hildas [Grav et al. 2012. ApJ 744, 197G, Grav et al. 2012. ApJ, 759 49G]. To take advantage of WISE 3.4-micron (W1) broad-band data, Ali-Lagoa et al. [2013. A&A 554A, 71A] combined them with complementary spectral data from the literature and showed that they can be used to detect the presence of the water-related 3-micron absorption features in a sufficiently numerous group of objects. We present the results of applying the same method to Hildas and JTs.