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The energy at which collective transverse flow in the reaction plane disappears, the balance energy E bal , is found to depend on the isospin of the system using the reactions 58 Fe 1 58 Fe and 58 Ni 1 58 Ni. The more neutron-rich system exhibits higher balance energies for all measured impact parameters, in agreement with the predictions of a transport model which incorporates an isospin dependent mean field and isospin dependent in-medium nucleon-nucleon cross sections.[S0031-9007 (97)02358-2] PACS numbers: 25.70.Pq, 25.75.Ld