We consider the novel paradigm of nanoscale transient communication (NTC), where certain components of the small-scale communication link are physically transient. As such, the transmitter and the receiver may change their properties over a prescribed lifespan due to their time-varying structures. The NTC systems may find important applications in the biomedical, environmental, and military fields, where system degradability allows for benign integration into life and environment. In this paper, we analyze the NTC systems from the channel-modeling and capacity-analysis perspectives and focus on the stochastically meaningful slow transience scenario, where the coherence time of degeneration Td is much longer than the coding delay Tc. We first develop novel and parsimonious models to characterize the NTC channels, where three types of physical layers are considered: electromagnetism-based terahertz (THz) communication, diffusion-based molecular communication (DMC), and nanobots-assisted touchable communication (TouchCom). We then revisit the classical performance measure of ϵ-outage channel capacity and take a fresh look at its formulations in the NTC context. Next, we present the notion of capacity degeneration profile (CDP), which describes the reduction of channel capacity with respect to the degeneration time. Finally, we provide numerical examples to demonstrate the features of CDP. To the best of our knowledge, the current work represents a first attempt to systematically evaluate the quality of nanoscale communication systems deteriorating with time.