The population stability of Baizongia pistaciae (Linnaeus) (Hemiptera: Aphididae) on its primary host, the tree Pistacia palaestina Boissier (Anachardiaceae), was investigated using 17-20 years of data from a study of gall abundance on individual trees in Israel. Abundance varied by at least an order of magnitude among adjacent trees, among locations, and among years. Stability was quantified for the alternate-year cohorts as population variability (PV) and persistence, at three spatial scales. PV (a proportion between 0 and 1) was similar between cohorts and declined with population scale - subpopulation (a tree): 0.676 ± 0.092 (±1 SD, n = 40); population: 0.581 ± 0.098 (±1 SD, n = 6); region: 0.424 (0.345 and 0.503, n = 2). Persistence (proportion of years that galls were present) was usually near 0.9, but 0.1 for some subpopulations, and 1.0 at the population and regional scales. Although protected within large galls on long-lived trees, the PV of B. pistaciae was similar to that of native, free-living aphid species on more ephemeral herbaceous hosts, but lower than for introduced aphid species. Persistence of B. pistaciae decreased as abundance decreased but not as PV increased. PV did not increase with the length of the study period; and declined with increasing population scale, because abundance was not synchronised among subpopulations or populations. PV was similar among populations, suggesting this parameter is characteristic of the species, although positive correlations between cohorts on a tree showed that PV was affected by the site-specific tree-grass habitats in which this species lives.