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Normal transitions and a subsequent quench were experienced with the pool-cooled helical coils of the Large Helical Device (LHD) during its excitation test. Although the initiated normal zone once started to recover, a disruptive transverse propagation followed and triggered an emergency discharging program. The cryogenic stability of the composite-type superconductor has been studied by sample experiments as well as by numerical calculations. Due to the rather long magnetic diffusion time constant in the pure Al stabilizer, transient stability of the conductor seems to play an important role for driving finite propagation of a normal zone. The cause of the final quench is also discussed from the viewpoint of cooling deterioration due to a possible accumulation of He bubbles.