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Two models of the high gradient 70 mm aperture superconducting low-/spl beta/ quadrupole magnets were developed at KEK as part of the collaboration between CERN and KEK for the Large Hadron Collider (LHC). The training tests of both model magnets have been carried out at 1.9 K and both models successfully reached the design field gradient of 240 T/m, and the training memory partially remained after thermal cycles. General characteristics of the training curve for the models seemed to be similar. In this paper, training results of the model magnets is described and discussed.