Ni-Ti shape memory alloys are known to demonstrate three possible transformation paths between B2 and B19' phases, B2-R-B19', B2-B19' and B2-B19-B19', depending on their composition and thermo-mechanical treatment. In this work the isothermal kinetics of accumulation of martensite/austenite for all types of martensitic transformations in Ni-Ti and Ni-Ti-X(X = Fe or Cu) has been studied by means of resistance measurements during interruption of cooling/heating scans. Experimental results show that all transformations to the B19' phase (B2-B19', R-B19', B19-B19') demonstrate a substantial isothermal accumulation of martensite during isothermal dwelling between the martensitic transformation start and finish temperatures. The reverse transformations B19'-R and B19'-B19 are also classified as isothermal. The isothermal accumulation of austenite detected during the reverse B19'-B2 transformation is much less intense, at least partially due to the low sensitivity of resistance to the martensite fraction variation during the reverse transformation, and remains comparable with the resolution of the experimental set-up. The transformations between the B2 and R as well as between the B2 and B19 phases are athermal. Analysis of the entire set of possible transformations in beta Ni-Ti systems allows one to conclude that isothermal transformations possess a much broader hysteresis and transformation range compared with athermal ones. Since the hysteresis of the transformation is related to the friction forces acting on interfaces this fact, and also observation of the isothermal effects during reverse martensitic and intermartensitic transformations, strongly support the interpretation of the observed isothermal effects in Ni-Ti as due to the diffusionless but thermally activated motion of interfaces during transformation. The difference between the transformation to B19' martensite (isothermal) and all others (athermal) is attributed to a distinction in strain accommodation. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.