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Aqueous foams are ubiquitous; they appear in products and processes that span the cosmetics, food, and energy industries. The versatile applicability of foams comes as a result of their intrinsic viscous and elastic properties; for example, foams are exploited as drilling fluids in enhanced oil recovery for their high viscosity. Recently, so-called capillary foams were discovered: a class of foams that have excellent stability under static conditions and whose flow properties have so far remained unexplored. The unique architecture of these foams, containing oil-coated bubbles and a gelled network of oil-bridged particles, is expected to affect foam rheology. In this work, we report the first set of rheological data on capillary foams. We study the viscoelastic properties of capillary foams by conducting oscillatory and steady shear tests. We compare our results on the rheological properties of capillary foams to those reported for other aqueous foams. We find that capillary foams, which have low gas volume fractions, exhibit long lasting rheological stability as well as a yielding behavior that is reminiscent of surfactant foams with high gas volume fractions.