In this third paper on magnetic clouds and their interaction with the terrestrial magnetosphere we focus on substorm activity attending the 30‐hour‐long passage of the magnetic cloud seen at 1 AU on January 14/15, 1988. Our main aim is to describe high resolution field and plasma data from six spacecraft at geostationary orbit and beyond (up to 9 RE), supplemented by ground magnetograms, in order to estimate the number of substorm onsets that occurred during this passage. This analysis, attempted here for the first time over such an extended data interval, enables us to obtain a comprehensive view of the magnetospheric behavior. We then relate the interplanetary field and plasma input to the magnetospheric and ionospheric output. The paper is a case study of the response of the nightside magnetosphere to particularly well‐behaved interplanetary conditions: the variations with time of the field and plasma parameters in the magnetic cloud are simple; and the north‐south (Bz) and east‐west (By) components of the magnetic field range slowly over ∼20 nT on both sides of zero. From a synopsis of the substorm observations we find that during the earlier 11‐h interval when Bz was continuously positive, the magnetosphere was quiescent, whereas in the later 18‐h interval, when Bz was uninterruptedly negative, a large magnetic storm was set off. In this latter interval the substorm onsets recur on average every 50 min. Their average recurrence frequency remains relatively undiminished even when the magnetic cloud Bz and other measures of the interplanetary energy input have decreased considerably. We find these results to concur with the current models of magnetospheric substorms based on deterministic nonlinear dynamics. Using ancillary information from HF radar observations of ionospheric convection, we investigate the magnetospheric conditions preceding the first substorm onset in the long substorm sequence. We find that it occurred when the cloud's magnetic field had a persistent northward component but was predominantly westward pointing.