Many networked human-machine interface systems have a distributed structure for certain purposes such as more computational power, tele-presence, collaboration, and portability. However, network delays are inevitable in the distributed structure, and often make sensory information delivered behind time to the user. In the literature, the effect of network delays on the quality of information presentation has been considered with respect to task performances in most cases. In this paper, we pay attention to a more stringent criterion, namely whether perceptual artifacts caused by network delays are perceptible by the user. We examined minimum perceptible visual and/or haptic rendering delays by measuring their discrimination thresholds between normal and delayed virtual environments with and without a task, and report the results in this paper. We also provide a simple guideline for determining whether active delay compensation algorithms are required in a networked human-machine interface system by comparing representative network delays to the measured discrimination thresholds.