The reaction of D-2 with NO on Rh(110) was studied by means of quadrupole mass spectrometry in combination with work function measurements (Delta Phi) and low-energy electron diffraction (LEED). A strong hysteresis of the D2O production was found in the temperature range between 650 and 1050 K. This effect was most pronounced for a partial pressure ratio D-2/NO = 1.2 at a total pressure in the 10(-6) mbar range. The different reactivities of the hysteresis loop were found to be correlated with variable oxygen coverages, Theta(0). This was concluded from the observation of specific LEED patterns, i.e. from the occurrence of an oxygen-induced c(2 X 8) pattern (Theta(0) similar to 0.85 monolayer) in the low-reactivity branch and, respectively, of a (1 X 1) Rh pattern with insignificant oxygen coverages in the high-reactivity branch. The change from low to high reactivity was found to involve transient c(2 X 6) and np(2 X 2) LEED patterns. Rate oscillations were found to occur with long periods, typically between 23 and 33 min, at 850-950 K. These oscillations could only be induced by a rapid change in the D-2/NO ratio from 1.2 to 0.85 (at a total pressure of 6.5 X 10(-6) mbar) and were stable for several hours with only slight variations in amplitude and frequency. Simultaneous measurements of the work function revealed a strong correlation with the D2O production rate, i.e. Delta Phi was high when the reaction rate was low and vice versa, indicating that the oscillations were associated with variations of the oxygen surface coverage. The results are discussed within a kinetic model of the catalytic cycle.