Field-induced magnetization jumps with similar characteristics are observed at low temperature for the intermetallic germanide Gd5Ge4 and the mixed-valent manganite Pr0.6Ca0.4Mn0.96Ga0.04O3. We report that the field location-and even the existence-of these jumps depends critically on the magnetic field sweep rate used to record the data. It is proposed that, for both compounds, the martensitic character of their antiferromagnetic-to-ferromagnetic transitions is at the origin of the magnetization steps. © 2004 The American Physical Society.