Relative to motorized devices, passive hip exoskeletons with elastic actuation provide cheaper and lower-profile solutions to assist locomotion during walking. However, the influence of elastic hip assistance on stability during walking is poorly understood. Here, we investigated the effects on stability of a hip exoskeleton that provided elastic flexion torque during late stance. We quantified stability using both sagittal whole-body angular momentum (WBAM) range and whole-body mechanical work during walking with unexpected anteroposterior treadmill belt accelerations among 11 healthy uninjured individuals. We hypothesized that during perturbations, 1) an elastic hip exoskeleton would improve stability as measured by a smaller range in sagittal WBAM and a lower whole-body energetic demand imposed by the perturbation, and 2) this improvement in whole-body energetic demand would be mediated by the exoskeleton shifting the local mechanical energetics of the hip joint to oppose the energetic demands of the perturbation. Contrary to our hypotheses, the elastic hip exoskeleton did not influence whole-body work demands imposed by perturbations (p>0.226). Additionally, while sagittal WBAM ranges were larger during unperturbed walking with increasing exoskeleton stiffness due to alterations in trunk kinematics (p<​0.001), this effect did not extend to perturbed walking (p>0.419). Further, while higher exoskeleton stiffnesses (0.66–1.0 Nm/deg) shifted ipsilateral hip joint work in opposition to whole-body work demands, the same stiffnesses shifted contralateral hip joint work toward whole-body work demands. Our findings demonstrate conclusions drawn about stability from sagittal WBAM range do not carry over from unperturbed to perturbed walking.