This paper discusses how epistemic uncertainties are considered in a number of different natural hazard areas including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. In each case it is common practice to treat most uncertainties in the form of aleatory probability distributions but this may lead to an underestimation of the resulting uncertainties in assessing the hazard, consequences and risk. It is suggested that such analyses might be usefully extended by looking at different scenarios of assumptions about sources of epistemic uncertainty, with a view to reducing the element of surprise in future hazard occurrences. Since every analysis is necessarily conditional on the assumptions made about the nature of sources of epistemic uncertainty it is also important to follow the guidelines for good practice suggested in the companion Part 1 by setting out those assumptions in a condition tree.