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We study the indirect detection of dark matter when the local dark mattervelocity distribution depends upon position, as expected for the Milky Way andits dwarf spheroidal satellites, and the annihilation cross-section is notpurely s-wave. Using a phase-space distribution consistent with the dark matterdensity profile, we present estimates of cosmic and gamma-ray fluxes from darkmatter annihilations. The expectations for the indirect detection of darkmatter can differ significantly from the usual calculation that assumes thatthe velocity of the dark matter particles follows a Maxwell-Boltzmanndistribution.

The impact of the phase-space density on the indirect detection of dark matter