Uncertainties in data and parameter values have often been ignored in hazard estimates based on historic and prehistoric records of rupture on fault segments. A mixture of distributions approach is appropriate to handle uncertainties in parameters of recurrence time distributions estimated from the geological and historical earthquake record of a fault segment, and a mixture of hazards approach is appropriate for data uncertainties and for uncertainties in parameters estimated from a set of similar faults. The former approach admits updating of the distributions for uncertainty as time passes. The aim is to present the hazard as a single value which takes account of both data and parameter uncertainties, conditional only on modeling assumptions. The proposed methods are described in detail for the exponential and lognormal recurrence time models for fault-rupturing earthquakes and applied, by way of illustration, to selected fault segments, namely, the Mojave segment of the San Andreas fault, California, and the Wellington-Hutt Valley segment of the Wellington fault, New Zealand. ¿ American Geophysical Union 1994