An investigation of etching behaviors for Mo and Al2O3 thin films in O-2/Cl-2/Ar inductively coupled plasmas at constant gas pressure (6 mTorr), input power (700 W) and bias power (200 W) was carried out. It was found that an increase in Ar mixing ratio for Cl-2/Ar plasma results in non-monotonic etching rates with the maximums of 160 nm/min at 60 % Ar for Mo and 27 nm/min at 20 % Ar for Al2O3. The addition of O-2 in the Cl-2/Ar plasma causes the non-monotonic Mo etching rate (max. 320 nm/min at 40-45 % O-2) while the Al2O3 etching rate decreases monotonically. The model-based analysis of etching kinetics allows one to relate the non-monotonic etching rates in Cl-2/Ar plasma to the change in the etching regime from the ion-flux-limited mode (at low Ar mixing ratios) to the neutral-flux-limited mode (for high Ar mixing ratios). In the Cl-2/O-2/Ar plasma, the non-monotonic Mo etching rate is probably due to the change in reaction probability.