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The angular momentum flux from an inspiralling binary system of compactobjects moving in quasi-elliptical orbits is computed at the thirdpost-Newtonian (3PN) order using the multipolar post-Minkowskian wavegeneration formalism. The 3PN angular momentum flux involves the instantaneous,tail, and tail-of-tails contributions as for the 3PN energy flux, and inaddition a contribution due to non-linear memory. We average the angularmomentum flux over the binary's orbit using the 3PN quasi-Keplerianrepresentation of elliptical orbits. The averaged angular momentum fluxprovides the final input needed for gravitational wave phasing of binariesmoving in quasi-elliptical orbits. We obtain the evolution of orbital elementsunder 3PN gravitational radiation reaction in the quasi-elliptic case. Forsmall eccentricities, we give simpler limiting expressions relevant for phasingup to order $e^2$. This work is important for the construction of templates forquasi-eccentric binaries, and for the comparison of post-Newtonian results withthe numerical relativity simulations of the plunge and merger of eccentricbinaries.

Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits