The morphologies of some martian gullies appear similar to terrestrial features associated with debris flow initiation, erosion, and deposition. On Earth, debris flows are often triggered by shallow subsurface throughflow of liquid water in slope-mantling colluvium. This flow causes increased levels of pore pressure and thus decreased shear strength, which can lead to slide failure of slope materials and subsequent debris flow. The threshold for pore pressure-induced failure creates a distinct relationship between the contributing area supplying the subsurface flow and the slope gradient. To provide initial tests of a similar debris flow initiation hypothesis for martian gullies, measurements of the contributing areas and slope gradients were made at the channel heads of martian gullies seen in three HiRISE stereo pairs. These gullies exhibit morphologies suggestive of debris flows such as leveed channels and lobate debris fans, and have well-defined channel heads and limited evidence for multiple flows. Our results show an area-slope relationship for these martian gullies that is consistent with that observed for terrestrial gullies formed by debris flow, supporting the hypothesis that these gullies formed as the result of saturation of near-surface regolith by a liquid. This model favors a source of liquid that is broadly distributed within the source area and shallow; we suggest that such liquid could be generated by melting of broadly distributed icy materials such as snow or permafrost. This interpretation is strengthened by observations of polygonal and mantled terrain in the study areas, which are both suggestive of near-surface ice.