Several previous calculations relating to rates of unimolecular isomerizations have led to satisfactory agreement with experiment only if it is assumed that there is a low efficiency of energy transfer on collision. Other evidence, however, indicates that collisions in unimolecular processes are "strong", having a high probability of transferring vibrational energy. This discrepancy is traced to the fact that previous treatments have neglected the back reaction, in which the highly energized isomer molecule is reconverted into a reactant molecule. In the present work the RRKM formulation of unimolecular reaction theory has been extended to take this back reaction into account. Calculations are made for the isomerizations of cis-butene-2, cyclobutene and cyclopropane. Agreement is good for the first two systems. For cyclopropane, calculations based on the assumption that a C-H stretch is the reaction co-ordinate still require a collision efficiency of 0.25 for agreement with experiment.