New data are presented on dynamic measurements of elasticity and anelasticity of several poly- and single crystalline Ni1+xTi1-x alloys for frequencies between 0.05 and 100 kHz over a wide temperature range below room temperature. Anelastic effects, previously attributed to "strain glass freezing", exist and are even intensified in alloys close to the equiatomic composition, which are not expected to demonstrate the "strain glass" state. We also compare the results of static zero-field-cooling and field-cooling experiments for normally transforming and non-transforming alloys and show that a strain maximum in static zero-field-cooling tests for high-Ni-content alloys attributed to "strain glass freezing" is due to elastic strain, which was not previously taken into account. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.