The resistance switching dynamics of TiN/HfO2/Pt devices is analyzed in this paper. When biased with a voltage ramp of appropriate polarity, the devices experience SET transitions from high to low resistance states in an abrupt manner, which allows identifying a threshold voltage. However, we find that the stimulation with trains of identical pulses at voltages near the threshold results in a gradual SET transition, whereby the resistive state visits a continuum of intermediate levels as it approaches some low resistance state limit. On the contrary, RESET transitions from low to high resistance states proceed in a gradual way under voltage ramp stimulation, while gradual resistance changes driven by trains of identical spikes cover only a limited resistance window. The results are discussed in terms of the relations among the thermo-electrochemical effects of Joule heating, ion mobility, and resistance change, which …