The distribution of the transport current in a twisted multifilamentary composite has been studied experimentally and theoretically by observing the terminal voltage during a sweep of the current for a sample configuration which simulates the windings of superconducting magnets. The theoretical analysis shows that the voltage versus transport current characteristics are directly related to the current distribution inside the composite conductor, and expressions of the voltage are derived for the highly non-uniform current distribution to be expected from the effect of the self-field. The observed voltage agrees well with the theoretical prediction up to a current level of about 60% of the critical current. At higher values an excess resistive voltage develops progressively. The influence of this addistional resistive state on the current distribution and on the self-field instability in discussed briefly.