The kinetics of HDO Surface and bulk diffusion on ultrathin (25-192 BL; 96-700 Angstrom) single-crystal (H2O)-O-16 ice multilayers were studied using a combination of laser-induced thermal desorption (LITD) probing and isothermal desorption depth-profiling. The single-crystal hexagonal ice multilayers were grown epitaxially on a single-crystal Ru(001) metal substrate with the basal (001) facet of ice parallel to the Ru(001) surface. HDO surface diffusion on the single-crystal ice multilayer was not observed within the resolution of the LITD experiment at T=140 K. These LITD surface diffusion experiments yielded an upper Limit to the HDO surface diffusion coefficient of D-s less than or equal to 1x10(-9) cm(2)/s at T= 40 K. The bulk diffusion coefficients were measured along the c axis of the hexagonal ice crystal which is perpendicular to the (001) plane. HDO was observed to diffuse readily into the underlying (H2O)-O-16 ice multilayer. The measured HDO bulk diffusion coefficients ranged from D = 2.2(+/-0.3)x10(-16) cm(2)/s to D=3.9(+/-0.4)x10(-14) cm(2)/s over the temperature range from 153 to 170 K. The HDO bulk diffusion coefficients-were measured for (H2O)-O-16 thicknesses of 25-192 BL (1 BL=1.06x10(15) molecules/cm(2)) and initial HDO adlayer thicknesses of 2-9 BL. The KDO bulk diffusion was independent of (H2O)-O-16 him thickness and initial HDO coverage. Arrhenius analysis of the temperature-dependent bulk diffusion coefficients yielded a diffusion activation energy of E-A =17.0+/-1.0 kcal/mol and a diffusion preexponential of D-0=4.2(+/-0.8)x10(8) cm(2)/s. Compared with extrapolations from macroscopic diffusion kinetics obtained earlier at temperatures close to the melting point, these bulk diffusion coefficients are larger and may reflect the perturbation of the ultrathin ice films induced by the nearby interfaces. The differences between these HDO diffusion kinetics and recently measured kinetics for (H2O)-O-16 indicate that H/D exchange and molecular transport make comparable contributions to the HDO diffusion coefficient.