The response characteristics of olfactory receptor neurons (ORNs) and their corollary, the differential sensitivity and the resolving power, are fundamental to understand olfactory coding and the information extracted from a fluctuating olfactory signal. Previous work has focused on the temporal resolution of odor pulses presented for very brief periods at varying concentrations. The time course of the odor pulses as a stimulus parameter has not been considered. The present study investigated the precision of the ON and OFF ORNs on the antennae of the cockroach to discriminate increments and decrements of continuously rising and falling odor concentrations. Stimulation consisted of ramp-like upward and downward concentration changes in a trapezoid fashion. By varying ramp steepness, we examined the effect of the rate of concentration change. Both ORNs were clearly dependent on continuously rising and falling odor concentrations. As the rate of upward and downward concentration changes increases, differential sensitivity improves. Since the scatter of responses around the stimulus-response functions also increases, the resolving power for concentration increments and decrements deteriorates. Thus, the slower the rate of concentration change, the higher the precision in differentiating small concentration changes. Intuitively, the inverse relationship between the rate of concentration change and the resolving power is not surprising because accuracy requires time. A high degree of precision at slow concentration rates enables the cockroach to use information about the onset and offset slopes of odor pulses in addition to the pulse height to encode the spatial-temporal structure of turbulent odor plumes.