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A new system was developed for measuring AC current distributions in high Tc superconducting tapes under an external AC magnetic field. In our measurement the current distributions are indirectly found from the results of the self-field distributions measured by an array of pickup coils located around the tape. For improved measurement accuracy under the external magnetic field, a compensation coil was used to cancel the component of the external magnetic field from the signal of pickup coil. In order to confirm the validity of this system, measurement of current distributions in a test conductor composed of insulated copper wires was carried out under an external AC magnetic field. Using this system, we measured the current distributions in multifilamentary Ag alloy sheathed Bi-2223 tape as a function of the angle of the external AC magnetic field at 77 K. Further, we investigated the characteristics of the current distributions for the case of a simultaneous application of AC transport current and transverse AC magnetic field. On the basis of the obtained results the practicality of our measurement system is discussed.