Heterogeneous reactions of HOCl + HCl --> Cl2 + H2O (1) and ClONO2 + HCl - Cl2 + HNO3 (2) on ice surfaces at a temperature of 188 K have been investigated in a flow reactor interfaced with a differentially pumped quadrupole mass spectrometer. Partial pressures for HOCl and ClONO2 in the range of 6.5 X 10(-8)-2.0 x 10(-6) Torr, which mimic conditions in the polar stratosphere, have been used. Uptake of HCI on ice surfaces using partial pressures of HCI in the range of 1.8 X 10(-7)-8.0 x 10(-6) Torr has been measured prior to contact with HOCl or ClONO2. Pseudo-first-order decays of HOCl and ClONO2 over HCl-coated ice surfaces have been observed in all experiments under the conditions of P(HOCl) < P(HCl) and P(ClONO2) < P(HCl) used. Both the decay rates of HOCl and ClONO2 and the growth rates of Cl2 have been used to obtain reaction probabilities: gamma(g) (1) = 0.34 +/- 0.20 (1sigma) and gamma(g) (2) = 0.27 +/- 0.19 (1sigma) if we assume that the area of ice surfaces is equal to the geometric area of the flow-tube reactor. The results are in good agreement with previous measurements. By considering the morphology of ice films, we obtain true reaction probabilities gamma(t)(1) = 0.13 +/- 0.08 and gamma(t)(2) = 0.10 +/- 0.08 using a previously published model of surface reaction and pore diffusion. In addition, the true reaction probability, gamma(t) (3), for the ClONO2 + H2O --> HOCl + HNO3 (3) reaction has been measured to be greater than 0.03 on ice surfaces. Reaction mechanisms for these heterogeneous reactions 1-3 are discussed, including a possible two-step mechanism for reaction 2 in terms of reaction 3 and reaction 1.