Tactile display is a technology that gives an artificial sense of touch to operators of information terminals or master-slave systems. The generation of tactile stimuli in response to the hand movements of the operators is associated with active touch and is considered to be one of the effective display methods, however which inevitably causes delayed tactile feedbacks from tactile displays. The knowledge of the detection threshold of system latency between the hand movements and the stimuli is helpful in designing the tactile displays. In this study, the identification of the thresholds through psychophysical experiments of 13 participants revealed two types of thresholds. One was the time-delay at which the participants observed the existence of latency. The other was the minimal time-delay that could affect the subjective feelings of the operators while they were not conscious of the latency. The means of the thresholds were 41 ms and 59 ms, respectively. The participants reported that the time-delay stimuli caused various changes in their subjective feelings. The empirical results suggest that the two types of thresholds depend on different sensory processes. This paper also proposes a design policy for tactile display systems in terms of system latency.