  We study the evolution of the eccentricity of an eccentric orbit with
spinning components. We develop a prescription to express the evolving
eccentricity in terms of initial eccentricity and frequency. For that purpose
we considered the spins to be perpendicular to the orbital plane. Using this we
found an analytical result for the contribution of spin in eccentricity
evolution. As a result, we expressed orbital eccentricity in a series of
initial eccentricity and gravitational wave frequency. The prescription
developed here can easily be used to find arbitrarily higher-order
contributions of initial eccentricity. With the eccentricity evolution at hand,
we computed the evolving energy and angular momentum fluxes for eccentric orbit
with spinning components. This result can be used to construct the waveforms of
spinning compact objects in an eccentric orbit.
