We study an aspect of substorm occurrence during Earth passage of the October 1995 magnetic cloud and the corotating stream overtaking it. The substorms were identified primarily by five latitudinal arrays of ground‐based magnetometers around the globe and the interplanetary observations were from the Wind spacecraft. The aspect we study is the energy and magnetic flux accumulated in the geomagnetic tail between successive substorm onsets, which we calculate by integrating different theoretical and empirical expressions for the solar wind‐magnetosphere coupling rates. These coupling functions, which depend strongly on the interplanetary magnetic field (IMF) north‐south component, Bz, have all been proposed previously as appropriate measures of solar wind input into the magnetosphere and indeed most correlate well with the cross‐polar cap potential. We contrast the effect on magnetospheric substorms of three solar wind states: A 14 hour long period of continuous and strong IMF Bz < 0 and a 16 hour long period of continuous and strong IMF Bz > 0, both states due to the magnetic cloud; and a 22 hour long period of intermittent IMF Bz polarity of large, but weaker amplitude, due to Alfvén waves in the faster stream. We find that (1) the average rate of substorm onset occurrence during the Bz < 0 phase in the cloud is higher than during the intermittent Bz polarity in the wake, by about a factor of 1.4. (2) The long Bz > 0 phase of the cloud elicited no substorm onsets. (3) The total time for which Bz is negative between substorm onsets is less variable than the interonset interval itself, but still varies between ∼ 0.5 hour and ∼ 4 hours. (4) The integral of any individual solar wind‐magnetosphere coupling function between successive substorm onsets is also variable. (5) The interonset integral varies differently for different coupling functions, even for those which measure the same quantity (energy or magnetic flux). (6) For all energy and magnetic flux coupling functions we find a positive correlation between the interonset integral and the value of the coupling function around the time of the preceding substorm onset. The correlation is best for the ε and υBs functions. This result is consistent with those substorm models in which substorm onset occurs at some fixed energy or magnetic flux threshold and where the amount of energy or magnetic flux lost following each substorm onset is proportional to the solar wind input rate at the time of onset.