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Transport current AC losses of superconducting cables of the (6+1) configuration (6 AC superconducting multifilamentary strands bundled around a CuNi center wire) and the single strand composing the cable were measured in an AC external magnetic field. The measured AC loss data of the cables of different twist pitches and directions were compared with those of the strand. It was shown that the transport current AC losses of the cables were affected by the twist directions and pitches of the cables. A theoretical model to evaluate the AC loss due to transport current was derived. In the model, the effect of the longitudinal magnetic field subjected to the strands and the current density vs. electric field characteristics of the strand were taken into consideration. Our theoretical model well explains the measured characteristics of the cable.