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Elastic constants of filled-skutterudite NdOs4Sb12 single crystals have been investigated by means of ultrasonic measurements. Transverse C44 and longitudinal C11 modes show Curie-type softening, which is proportional to the reciprocal temperature from 10K down to 0.9K. This softening can be explained in terms of the quadrupolar susceptibility modified by crystalline electric field with a Γ8 quartet...