ABSTRACTThe epidemic-type aftershock sequence model with tapered Gutenberg–Richter (ETAS-TGR)-distributed seismic moments is a modification of the classical ETAS-GR (without tapering) proposed by Kagan in 2002 to account for the finiteness of the deformational energy in the earthquake process. In this article, I analyze the stability of the ETAS-TGR model by explicitly computing the relative branching ratio ηTGR: it has to be set less than 1 for the process not to explode, in fact in the ETAS-TGR model, the critical parameter equals the branching ratio as it happens for the ETAS-GR, due to the rate separability in the seismic moments component. When the TGR parameter βk=23ln10β is larger than the fertility parameter αk=23ln10α, respectively obtained from the GR and the productivity laws by translating moment magnitudes into seismic moments, the ETAS-TGR model results to have less restrictive nonexplosion conditions than in the ETAS-GR case. Furthermore, differently from the latter case in which it must hold β>α for ηGR to exist finite, any order relation for βk and αk (equivalently, for β,α) is admissible for the stability of the ETAS-TGR process; indeed ηTGR is well defined and finite for any βk,αk. This theoretical result is strengthened by a simulation analysis I performed to compare three ETAS-TGR synthetic catalogs generated with βk⋚αk. The branching ratio ηTGR is shown to decrease as the previous parameter difference increases, reflecting: (1) a lower number of aftershocks, among which a lower percentage of first generation shocks; (2) a lower corner seismic moment for the moment–frequency distribution; and (3) a longer temporal window occupied by the aftershocks. The less restrictive conditions for the stability of the ETAS-TGR seismic process represent a further reason to use this more realistic model in forecasting applications.