Magnetic relaxation experiments at low temperatures were performed in different zero‐field‐cooled (ZFC) and field‐cooled (FC) high‐Tc superconductors (HTSCs): TlBaCaCuO (2212 and 2223 phases, polycrystalline and thin‐film samples), (Hg,Tl)BaCaCuO (1223 phase, polycrystalline material), and (Bi,Pb)SrCaCuO (2212 phase, single crystal). For each system and in the whole temperature range investigated, the relaxation curves obtained after both cooling processes are linear with the logarithm of time. The temperature dependence of the relaxation rate normalized to the first magnetization value, R=∥d(M/M0)/d ln(t)∥, follows a trend which is common to all systems: R decreases linearly with decreasing temperature down to a value, which is called the crossover temperature, below which it levels off to a T‐independent plateau. This behavior gives evidence of a transition in the mechanism responsible for the relaxation process at low temperatures, from thermally activated (linear dependence on T) to quantum vortex motion (T‐independent regime). The experimental values for the crossover temperatures and normalized relaxation rates compare fairly well to numerical estimates in the framework of the theories of quantum vortex motion in layered HTSCs. Finally, the transition from one regime into another was studied in two samples of the TlBaCaCuO, 2223 phase, system in order to investigate the influence of dissipation on the quantum process. A clear conclusion on this point could not be drawn from these kinds of measurements. © 1996 American Institute of Physics.